Calculation Details & Engineering Reference
| Step | Equation | Substitution | Result |
|---|---|---|---|
| Enter valid process data to see the worked calculation. | |||
| Quantity | Equation |
|---|---|
| Heat duty | Q = ṁ · cp · (Tout − Tin) |
| LMTD (isothermal bath) | LMTD = (ΔT₁ − ΔT₂) / ln(ΔT₁/ΔT₂), ΔT₁ = Tbath−Tin, ΔT₂ = Tbath−Tout |
| Heat transfer area | A = Q / (U · LMTD) |
| Tube length | L = A / (π · Do) |
| Coil circumference | C = π · Dcoil |
| Number of turns | N = Ltube / C |
| Coil height | Hcoil = N · pitch |
| Water volume | V = (π/4) · D² · H · fill |
| Water mass | m = ρ · V |
| Burner capacity | P = Q / η · (1 + margin) |
| Fuel consumption | F = P / LHV |
The bath is treated as an isothermal heat source (well-mixed, burner-controlled). U is the overall coefficient referred to the tube outside area. Parallel tubes are wound as a multi-start helix, so they share one coil height.
Why heat the gas at all
Every bar of pressure cut across the regulator cools natural gas by roughly 0.5 °C (Joule-Thomson). A 40 → 20 bar station loses ~10 °C at the regulator — start from a cold winter inlet and the gas dives below its hydrate point, freezing the regulator internals. The heater raises the gas temperature before the cut so the downstream temperature stays safely above hydrate and dew point.
Why an indirect water bath
Firing a burner directly against a high-pressure gas coil creates hot spots and a real explosion risk. A water bath decouples them: the fire tube heats the water, the water heats the coil, and the water's mass smooths out control swings. The bath temperature is limited to ~95 °C so it never boils at atmospheric pressure.
What controls the size
The approach temperature ΔT₂ (bath minus gas outlet) drives everything: halve it and the LMTD drops, so the area — and coil length — grow fast. A bath 20 °C above the gas outlet is a comfortable design point. The overall U is dominated by the gas-side film; more parallel tubes lower gas velocity and U, so don't split the flow more than needed to fit the coil in the tank.
The burner margin
The 20% margin isn't padding — it covers shell heat loss to ambient, the cold-start transient (heating tonnes of water), and burner turndown so the control valve isn't pinned at 100%. The cold-start time shown uses this net margin as the available surplus power.
Enough that after JT cooling the gas stays above its hydrate formation temperature with margin — commonly the target is 15–20 °C downstream of the regulator. Work backwards: downstream target + 0.5 °C/bar × pressure drop = heater outlet.
You're closing the approach: as Tout nears Tbath, ΔT₂ → 0 and the LMTD collapses, so A = Q/(U·LMTD) diverges. Raise the bath temperature instead — or accept a lower outlet.
Barely — the wall ΔT step in the calculation details shows it. Even stainless (k ≈ 16 W/m·K) adds well under 1 °C across the wall at these fluxes. Material choice is about corrosion and code compliance, not heat transfer.
Not yet — it's a planned module. Rule of thumb: keep gas velocity under ~20 m/s in the coil; more parallel tubes cut both velocity and pressure drop. Use the Pressure Drop calculator for a first estimate on the equivalent straight length.