FEA / Structural Checks — GASCO Fired Heater Suite

F1 — Refractory 1D Finite Element Analysis

Galerkin 1D FEM through multi-layer refractory wall. Solves steady-state heat conduction with convection boundary conditions at both faces. Up to 6 layers, 50 nodes total. Reference: Incropera & DeWitt 7th Ed. §3.3; ASTM C680; API 560 §11.4.

Firebox gas temperature T_gas (°C)Inside radiant section — typically 800–1100°C for hot-oil heaters

Inside convection h_inner (W/m²K)Gas-side: natural convection + radiation ~15–25 W/m²K inside firebox. Radiation dominant at high T.

Ambient temperature T_amb (°C)

Outside convection h_outer (W/m²K)Forced wind: 10–20 W/m²K. Still air: 5–10 W/m²K. Use 8 for sheltered outdoor.

Wind speed (m/s)0 = still air; recalculates h_outer via Churchill-Bernstein on casing

Layer definition — up to 6 layers (hot face → cold face)

FEM equations & references ▾

1D steady: d/dx[k(x)·dT/dx] = 0 → Galerkin FEM with linear elements Element stiffness: K_e = k/L_e × [1 -1; -1 1] BC hot face: q_in = h_inner(T_gas - T_1) → modify K[0,0] += h_inner; f[0] += h_inner×T_gas BC cold face: q_out = h_outer(T_N - T_amb) → modify K[N,N] += h_outer; f[N] += h_outer×T_amb Solve: K·T = f by Thomas algorithm (tridiagonal) h_outer (Churchill-Bernstein): Nu = [0.60 + 0.387·Ra^(1/6)/(1+(0.559/Pr)^(9/16))^(8/27)]² × k_air/L_cas

API 560 §11.4: casing T ≤ 80°C (personnel protection). ASTM C680: heat loss per unit area calculation method. Incropera & DeWitt 7th Ed. §3.3: composite wall FEM. API 936 §4: refractory qualification and thermal performance.

Enter layer data and click Run FEM Analysis

Temperature profile through refractory wall

Layer-by-layer FEM results

API 560 §11.4 compliance check

F2 — Tube Wall Lamé Thermal + Pressure Stress

Thick-walled cylinder under internal pressure (Lamé equations) plus thermal gradient stress (plane strain). Circumferential, radial, and axial stresses at inner and outer wall. Von Mises combined stress vs API 530 allowable. Reference: API RP 530 §4; Timoshenko & Goodier "Theory of Elasticity" §131.

Tube OD (mm)

Wall thickness t (mm)Nominal — from M6/API 530 calculation

Internal design pressure P (barg)

Process fluid bulk temperature T_bulk (°C)

Inside film coefficient h_i (W/m²K)Liquid hot-oil: 600–1000 W/m²K. Gas phase: 80–200 W/m²K.

Average radiant flux q_avg (W/m²)From M15 Lobo-Evans calculation

Peak flux factor F_maxWimpress: 1.35 at s/d=2.0; 1.22 at s/d=3.0

Material properties

Tube material

Young's modulus E (GPa)

Thermal expansion α (×10⁻⁶/°C)

Thermal conductivity k_tube (W/mK)

Poisson's ratio ν

API 530 allowable stress S_allow (MPa)From API 530 Annex D at design T. A106B at 300°C: ~103 MPa. P11 at 400°C: ~100 MPa.

Lamé equations reference ▾

Lamé hoop: σ_θ(r) = P·ri²/(ro²-ri²) × (1 + ro²/r²) Lamé radial: σ_r(r) = P·ri²/(ro²-ri²) × (1 - ro²/r²) Thermal hoop: σ_θ_th = α·E·ΔT/(2(1-ν)) × [1 + ri²/ro² - 2ri²/(ro²-ri²)·ln(ro/ri)/ln(ro/ri)] Von Mises: σ_VM = √(σ_θ² + σ_r² - σ_θ·σ_r + 3·τ²) [τ=0 for axisymmetric] Peak tube metal T: T_wall = T_bulk + q_peak/h_i + q_peak·t/k_tube

API RP 530, 7th Ed. 2015 §4.2: tube metal temperature. Timoshenko & Goodier "Theory of Elasticity" §131 (thick cylinder). ASME Section VIII Div.1 UG-27 (thin shell comparison).

Enter tube and loading data

Stress distribution through tube wall

Stress results — inner, mid-wall, outer

API 530 compliance

F3 — Convection Tube VIV + Acoustic Resonance Check

Checks for flow-induced vibration (vortex shedding, Weaver-Fitzpatrick fluidelastic instability) and acoustic standing wave resonance in the convection tube bank. Reference: HTRI Xfh §5.3; Weaver & Fitzpatrick (1988); Blevins "Flow-Induced Vibration" 2nd Ed. (1990) §7.2; API 560 §6.3.8.

Tube OD d_o (mm)

Tube wall thickness t (mm)

Tube span (unsupported length) L_span (m)Distance between tube supports / corbels. Longer span → lower natural frequency → higher VIV risk.

Transverse pitch S_T (mm)Centre-to-centre perpendicular to flow

Longitudinal pitch S_L (mm)Centre-to-centre in flow direction

Tube arrangement

Flue gas flow conditions at convection section

Flue gas velocity (maximum face velocity) V_max (m/s)At minimum free area. V_max = W_fg / (ρ_fg × A_min). Typically 4–12 m/s.

Flue gas density ρ_fg (kg/m³)At mean FG temperature. Typically 0.35–0.55 kg/m³ at 400–700°C.

Flue gas viscosity μ (cP)At mean temperature. Typically 0.035–0.055 cP at 400–700°C.

Speed of sound in FG at mean T (m/s)c = √(γRT/MW). At 500°C: ~550 m/s. At 300°C: ~480 m/s.

Convection box width W_box (m)Internal clear width perpendicular to tube axis. Acoustic resonance f_1 = c/(2·W_box).

Tube material & support properties

Tube material Young's modulus E (GPa)

Tube material density ρ_tube (kg/m³)CS: 7850; 316SS: 8000; P11: 7850

Damping ratio ζ (log decrement δ = 2πζ)Bare tube in gas: ζ ≈ 0.002–0.005. With process fluid (liquid): ζ ≈ 0.02–0.05. Use 0.002 for conservative.

Number of tube rows N_rowsUsed for acoustic resonance assessment — deeper banks amplify acoustic response.

VIV equations & references ▾

Strouhal: f_vs = St × V_max / d_o [St=0.22 staggered, 0.19 inline] Natural freq: f_n = (π/2L²) × √(EI/ρ_total·A) where ρ_total = m_tube + m_fluid Lock-in zone: 0.7×f_n ≤ f_vs ≤ 1.3×f_n → VIV risk Reduced velocity: U_r = V_max / (f_n × d_o) Weaver-Fitzpatrick stability: U_r < K × (2πζ·m_total / (ρ_fg·d_o²))^0.5 → safe Acoustic: f_ac_n = n·c / (2·W_box) for modes n=1,2,3... Resonance risk: |f_vs - f_ac| / f_ac < 0.20 → acoustic resonance possible

Weaver & Fitzpatrick (1988) J.Fluids & Structures 2, pp.125-144. Blevins R.D. (1990) "Flow-Induced Vibration" 2nd Ed. Van Nostrand Reinhold §7.2. API 560 §6.3.8: convection tube span limits. HTRI Xfh Technical Manual §5.3.

Enter tube and flow data

Frequency map — vortex shedding vs natural frequency

VIV assessment results

Acoustic resonance check

Recommendations

F4 — Heater Terminal Nozzle Load Check

Checks inlet and outlet nozzle loads against API 560 Table 7–10 allowables. Applies 2× multiplier per ADNOC AGES-SP-09-004 / 50191C specification. WRC-297 simplified local stress index for nozzle-pipe junction. Reference: API STD 560 5th Ed. Tables 7–10; WRC Bulletin 297 (1987); ASME B31.3.

Nozzle pipe size (NPS, inches)

Nozzle schedule / wall thickness

Apply 2× ADNOC multiplier?

Applied loads — inlet nozzle

F_x (N)Axial force

F_y (N)Lateral force

F_z (N)Vertical force

M_x (N·m)Torsional moment

M_y (N·m)Bending moment

M_z (N·m)Bending moment

Applied loads — outlet nozzle

F_x (N)

F_y (N)

F_z (N)

M_x (N·m)

M_y (N·m)

M_z (N·m)

API 560 allowable load basis ▾

API STD 560, 5th Ed. 2016 Tables 7 & 8 (tube nozzle forces/moments) and Tables 9 & 10 (manifold nozzle forces/moments). Values are based on pipe OD and schedule. The ADNOC specification (AGES-SP-09-004 and project addenda) requires heater terminals to be designed for 2× the API 560 tabulated values. WRC Bulletin 297 (1987) provides the local stress index method for nozzle-pipe junctions used in detailed compliance assessment.

Enter applied loads and nozzle size

API 560 Table 7–10 allowable loads

Inlet nozzle — load check

Outlet nozzle — load check

Resultant force & moment vectors

F5 — Coil Thermal Expansion & Expansion Loop Sizing

Calculates thermal expansion per coil pass, differential expansion between radiant and convection coils, and required expansion loop leg dimensions. Reference: ASME B31.3 §319.4; CAESAR II beam theory; Peng & Peng "Pipe Stress Engineering" (2009) Ch.5.

Tube material

Mean coefficient of thermal expansion α (×10⁻⁶/°C)

Installation (cold) temperature T_cold (°C)

Radiant coil

Radiant coil effective length L_rad (m)Total tube arc length in radiant section = N_tubes × π × TCD (approx) or N × L for vertical tubes

Radiant coil design temperature T_rad (°C)Max tube metal temperature from M17

Convection coil

Convection coil effective length L_conv (m)

Convection coil design temperature T_conv (°C)

Crossover pipe & external piping

Crossover pipe length L_cross (m)

Crossover design temperature T_cross (°C)

Pipe OD for loop sizing (mm)

Pipe wall thickness (mm)

Young's modulus E at design T (GPa)

ASME B31.3 allowable stress S_allow (MPa)

Expansion equations ▾

Thermal expansion: ΔL = α × L × (T_design - T_install) Expansion loop (U-bend): L_leg = √(3·E·I·Δ / (2·S_allow·Z)) where I = π(OD⁴-ID⁴)/64, Z = I/(OD/2) = section modulus Loop leg simplified: L_leg ≥ √(3·D·Δ) for initial estimate (Peng & Peng)

ASME B31.3-2022 §319.4.1 flexibility analysis. Peng & Peng "Pipe Stress Engineering" (2009) Ch.5 expansion loop sizing. ASME Code Case N-318 interpolation for CTE values. API 560 Annex B: recommended practices for expansion loops in fired heater coil connections.

Enter coil geometry and temperatures

Expansion visualisation — all sections

Thermal expansion — bar chart

Thermal expansion per section

Expansion loop sizing — crossover pipe

CTE reference table for common materials

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