Cannabis Extraction Thermodynamics — Heat Load & Heat Exchanger Sizing

Link to Extraction Thermodynamics (Gray Wolf)

Summary

This guide explains how to estimate the heating and cooling loads in cannabis extraction systems and how to size heat exchangers for LPG (typically a 70:30 n-butane:n-propane mix) and ethanol. It walks through key thermodynamic concepts, useful constants, and worked examples so you can calculate BTU loads, coil length, and coolant requirements for your process.

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Quick Facts

• Category: Technical Reference / Thermodynamics
• Applies To:
  • Subzero LPG extraction (n-butane, isobutane, propane, 70:30 blends)
  • Subzero ethanol extraction
  • Chilling and recovery system design
• Key Concepts Covered:
  • Specific heat (BTU/lb/°F)
  • Heat of vaporization
  • Specific gravity and weight per volume
  • Boiling point and vacuum effects
  • Delta T (temperature difference)
  • Heat transfer coefficient (K value) for 304 SS
  • BTU/hr vs BTU/min and residence time
• Use Cases:
  • Sizing chillers and dry ice/LN₂ baths
  • Sizing stainless heat exchanger coils
  • Estimating dry ice usage
  • Estimating how much LPG must be evaporated to cool tanks
  • Understanding insulation losses

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1. Why Thermodynamics Matters in Extraction

Closed-loop LPG and ethanol systems often run well below 0°F, especially during:

• Solvent chilling for extraction
• Recovery tank chilling
• Solvent recovery and re-condensing

In almost all setups, you have a cold-side coolant (dry ice, LN₂, or chiller fluid) on one side of a stainless membrane (tank jacket, tubing wall, or plate) and process fluid (LPG or ethanol) on the other.

Understanding thermodynamics lets you:

• Estimate how many BTUs you need to remove or add
• Decide how big your heat exchanger must be
• Choose between dry ice baths, LN₂, or mechanical chillers
• Predict recovery rates and bottlenecks

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2. Core Thermodynamic Concepts

2.1 Total Heat Energy (Q)

Total heat moved in a process is represented as Q (in BTUs).

For temperature change (no phase change):

• Q = lbs of liquid × Specific Heat (BTU/lb/°F) × ΔT

Example (70:30 LPG mix):

• 1 lb of 70:30 LPG
• Specific heat ≈ 0.39 BTU/lb/°F
• ΔT = 164°F
• Q = 1 lb × 0.39 × 164 = 64 BTU

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2.2 Heat of Vaporization

When you boil a liquid into vapor (as in recovery), you must add extra energy beyond simple heating:

• Q = lbs of liquid × Heat of Vaporization (BTU/lb)

Example (70:30 LPG mix):

• 1 lb
• Heat of vaporization ≈ 171.1 BTU/lb
• Q = 1 lb × 171.1 = 171.1 BTU

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2.3 Specific Gravity and Weight per Volume

You’ll often know volume but need weight:

• lbs per cubic inch = 0.0361 × Specific Gravity

Examples:

• • n-Butane (SG = 0.601): 0.0361 × 0.601 ≈ 0.0217 lb/in³
  • 70:30 LPG mix (SG ≈ 0.548): 0.0361 × 0.548 ≈ 0.0198 lb/in³
  • Ethanol (SG = 0.787): 0.0361 × 0.787 ≈ 0.0284 lb/in³

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2.4 Boiling Points (Atmospheric Pressure)

At 1 atm (14.7 psia), approximate boiling points:

• n-Butane: 30.2°F
• Isobutane: 10.9°F
• Propane: –42.2°F
• 70:30 mix: ~–42.2°F (fractional behavior)
• Ethanol:  173.1°F

Reducing pressure lowers the boiling point; increasing pressure raises it.

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2.5 Delta T (Temperature Difference)

Delta T (ΔT) is the temperature difference across a heat exchanger.

For subzero cooling from ambient (70°F):

• ΔT = (Ambient °F) + (|Cold Side °F|)

Examples:

• Dry ice slurry near –94°F
  • ΔT = 70 + 94 = 164°F (often approximated in examples as ~179°F using sublimation temp)
• LN₂ at –320°F
  • ΔT = 70 + 320 = 390°F

As ΔT decreases along the coil, heat transfer rate drops, so average ΔT is used:

• Average ΔT = (ΔT at inlet + ΔT at outlet) / 2

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2.6 K Value of 304 Stainless Tubing

The thermal conductivity (K) of 304 stainless at ~68°F:

• K ≈ 14.4 BTU/ft²/hr/°F

For ½" OD × 0.049" wall 304 SS tube:

• Interior transfer area ≈ 0.1053 ft² per linear foot
• Transfer rate per foot:
  • 1.52 BTU/hr/°F per linear foot
  • (= 0.10528 ft² × 14.4 BTU/ft²/hr/°F)

Heat transfer formula:

• Q = K × Area (ft²) × ΔT × Time (hours)

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3. Useful Numbers for LPG and Ethanol

3.1 Specific Heat (BTU/lb/°F)

• n-Butane / Isobutane / Propane: 0.39
• Ethanol: 0.614

3.2 Heat of Vaporization (BTU/lb)

• n-Butane, Isobutane: 165.6
• Propane: 184
• 70:30 LPG mix: 171.1
• Ethanol: 364

3.3 Cooling Loads Example (70:30 Mix)

Chill 1 lb of 70:30 mix to –58°F:

Start Temp	Target Temp	ΔT (°F)	BTU/lb (0.39 × ΔT)
32°F	–58°F	90°F	35.1 BTU/lb
70°F	–58°F	128°F	50 BTU/lb

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4. Example Calculations

Example 1 — Chilling LPG Before Injection

Goal: Chill 3 column volumes of LPG from 70°F to –58°F in 4.5 minutes.

Assumptions:

• Column: 4" diameter × 36" tall
• 3 column volumes per cycle
• Injection time: 4.5 minutes = 0.075 hours
• Solvent: 70:30 LPG mix
• Specific heat: 0.39 BTU/lb/°F

Steps:

1. Column volume

• Volume (one column) = (π × r² × h)
• = (4" × 4" × 0.7854) × 36" ≈ 452.3 in³
• 3 volumes ≈ 1,357 in³
  

2. Weight of LPG

• Weight = 1,357 in³ × 0.019765 lb/in³ ≈ 26.8 lbs

3. BTU removal needed

• ΔT = 70 + 58 = 128°F
• Q = 26.8 lb × 0.39 × 128 ≈ 133.8 BTU

4. Required capacity

• Q/hr = 133.8 BTU / 0.075 hr ≈ 1,784 BTU/hr

You’d size your chiller or coil to handle at least ~1,800 BTU/hr for this step.

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Example 2 — Recovering 1 lb/min of 70:30 LPG with a Pump

Assumptions:

• 1 lb/min = 60 lb/hr
• Pump discharge: 180°F
• Final solvent temp: –42.2°F
• ΔT = 180 + 42.2 = 222.2°F
• Specific heat: 0.39 BTU/lb/°F
• Heat of vaporization: 171.1 BTU/lb

Specific heat portion:

• Q_SH = 60 lb × 0.39 × 222.2 ≈ 5,199 BTU/hr

Vaporization portion:

• Q_HV = 60 lb × 171.1 ≈ 10,266 BTU/hr

Total load:

• Q_total ≈ 5,199 + 10,266 = 15,465–15,983 BTU/hr (depending on rounding)

So the recovery condenser plus coolant system must reject roughly 16,000 BTU/hr.

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Example 3 — Coil Length Needed with Dry Ice Slurry

Goal: Remove 13,827 BTU/hr using a ½" 304 SS coil in a dry ice bath.

Given:

• Entry ΔT: 110°F vapor vs –95°F bath = 205°F
• Exit ΔT: –43°F vs –95°F = 52°F
• Average ΔT = (205 + 52) / 2 ≈ 128.5°F
• Transfer capability: 1.52 BTU/hr/°F per foot

Required length:

• Q = 13,827 BTU/hr
• Per-foot capacity = 1.52 × 128.5 ≈ 195.3 BTU/hr/ft
• Length = 13,827 / 195.3 ≈ 71 ft of ½" 304 SS tubing

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Example 4 — Coil Length Needed with LN₂

Same load (13,827 BTU/hr), but with LN₂ at –320°F:

• Entry ΔT: 110 + 320 = 430°F
• Exit ΔT: 320 – 43 = 277°F
• Average ΔT = (430 + 277) / 2 ≈ 353.5°F
• Per-foot capacity = 1.52 × 353.5 ≈ 537 BTU/hr/ft
• Length = 13,827 / 537 ≈ 26 ft of ½" 304 SS tubing

Takeaway: LN₂’s larger ΔT dramatically reduces required coil length.

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Example 5 — Dry Ice Needed to Chill Ethanol

Goal: Cool 5 gallons of ethanol from 70°F to –94°F with dry ice.

Assumptions:

• Ethanol SG: 0.787
• Specific heat: 0.614 BTU/lb/°F
• Dry ice ≈ 270 BTU/lb
• 1 gallon = 231 in³

Steps:

1. Volume: 5 × 231 = 1,155 in³
2. Weight: 1,155 × 0.0361 × 0.787 ≈ 32.8 lbs
3. ΔT: 70 + 94 = 164°F
4. BTU to remove: 32.8 × 0.614 × 164 ≈ 3,303 BTU
5. Dry ice required: 3,303 / 270 ≈ 12.2 lbs

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5. Using Evaporation to Cool Tanks

You can cool a tank of LPG by boiling off a portion of the solvent and using its heat of vaporization.

Example — Cool n-Butane Tank from 70°F to 30.2°F

Assumptions:

• “100 lb” water-capacity cylinder at 80% fill
• n-Butane SG = 0.601
• Heat of vaporization = 165.6 BTU/lb
• Specific heat = 0.39 BTU/lb/°F

Steps:

1. Liquid weight: 100 × 0.601 × 0.80 ≈ 48 lb
   
2. ΔT: 70 – 30.2 = 39.8°F
   
3. BTU removed: 48 × 0.39 × 39.8 ≈ 745 BTU
   
4. Pounds to evaporate: 745 / 165.6 ≈ 4.5 lb

So evaporating about 4.5 lb of butane will cool that tank from 70°F to ~30°F.

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6. Insulation and BTU Losses

You can estimate heat gain (or loss) through an insulated column using:

• R value (thermal resistance)
• K value (thermal conductivity, K = 1/R)

Rough guideline for a 4" × 36" column with 6" × 34" jacket:

• Surface area ≈ 6.7 ft²

Examples:

• Stainless + 1" foam (R ≈ 4):
  
  • Net K ≈ 0.25 BTU/hr/ft²/°F
  • At ΔT = 112.2°F → ~28.1 BTU/hr/ft²
  • Total loss ≈ 188 BTU/hr
    
• Stainless + 1" vacuum panel (R ≈ 25):
  
  • Net K ≈ 0.04 BTU/hr/ft²/°F
  • Loss ≈ 30 BTU/hr for full column

Takeaway: Better insulation significantly reduces cooling load.

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7. Practical Design Tips

• Always include safety margins. Use rounded-up BTU/hr loads when sizing equipment.
• Watch residence time. Shorter residence = higher BTU/hr requirement.
• Use average ΔT for coil sizing; inlet ΔT alone will overestimate capacity.
• Dry ice vs LN₂ vs chiller:
  
  • Dry ice: strong, but batch-based and manual.
  • LN₂: very powerful, great for compact HX, but more complex logistics.
  • Chiller: continuous, but must be correctly sized for BTU/hr.
• Insulate everything cold: Lines, columns, and tanks to reduce ongoing BTU load.

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