Catalytic Reactor Engineering, ULSD Hydrotreating & SAF Hydroprocessing
Hydrotreater LHSV, WHSV & Catalyst Bed Inventory Formula
Calculate Required Catalyst Bed Volume V_cat (m³) from LHSV, Loaded CoMo/NiMo Catalyst Mass (metric tons), True Weight Hourly Space Velocity WHSV (hr^-1), and Apparent Space Time (min).
LHSV and WHSV are NOT equal unless oil density happens to match packed catalyst bulk density!
Refinery Ultra-Low-Sulfur Diesel (ULSD) hydrotreaters and Sustainable Aviation Fuel (SAF) HEFA hydrodeoxygenation reactors specify kinetic severity via Liquid Hourly Space Velocity LHSV = Q_liquid_15C / V_catalyst_bed (m³ liquid/hr per m³ bulk loaded catalyst, hr^-1) or Weight Hourly Space Velocity WHSV = m_dot_feed / m_catalyst (kg feed/hr per kg catalyst, hr^-1)! Engineers frequently treat LHSV and WHSV as interchangeable—forgetting the exact density bridge WHSV = LHSV * (rho_liquid / rho_catalyst_bulk)! When light renewable vegetable oil or diesel (SG = 0.85 -> 850 kg/m³) flows over dense NiMo/alumina extrudates (750 kg/m³) vs dense grading beds (1,100 kg/m³), swapping LHSV for WHSV mis-sizes reactor catalyst tonnage by 13%–30%!
Verify on a 120.0 m³/hr (~18,100 bbl/d) Diesel ULSD Hydrotreater—Liquid_Feed_Rate Q = 120.0 m³/hr (B2), Feed_Specific_Gravity SG = 0.85 (850 kg/m³, B3), Design_LHSV = 1.50 hr^-1 (B4), and Catalyst_Bulk_Density rho_cat = 750.0 kg/m³ (B5): Required Loaded Catalyst Volume V_cat = 120 / 1.50 = 80.00 m³ (E2), Catalyst Charge Mass equals (80 * 750) / 1,000 = 60.00 metric tons (E3), True WHSV hits 1.50 * (850 / 750) = 1.70 hr^-1 (E4), and Apparent Bed Space Time (60 / LHSV) equals 40.00 minutes (E5)!
| Hydrotreater Catalyst KPI (120 m³/hr, SG=0.85, LHSV=1.5 hr^-1, rho_cat=750) | Formula | Verified Output |
|---|---|---|
| Required Catalyst Bed Volume (m³) | Liquid_Feed_m3_hr / Design_LHSV | 80.00 m³ (150.00 m³ @ LHSV = 0.8) |
| Loaded Catalyst Mass (metric tons) | (Catalyst_Vol_m3 * Bulk_Dens_kg_m3) / 1000 | 60.00 t (112.50 t @ LHSV = 0.8) |
| Weight Space Velocity WHSV (hr^-1) | LHSV * ((Feed_SG * 1000) / Bulk_Dens) | 1.70 hr^-1 (0.91 @ LHSV = 0.8) |
| Apparent Bed Space Time (min) | 60 / Design_LHSV | 40.00 min (75.00 min @ LHSV = 0.8) |
LHSV-to-WHSV Bridge & Reactor Catalyst Tonnage Formula
Validate Liquid_Feed > 0, Feed_SG in [0.50, 1.25], Design_LHSV in (0.05, 20.0], and Catalyst_Bulk_Density in [300, 1800] kg/m³!
=LET(qf_l, B2, sg_f, B3, lh_s, B4, rh_c, B5, IF(OR(qf_l <= 0, sg_f < 0.5, sg_f > 1.25, lh_s <= 0.05, lh_s > 20, rh_c < 300, rh_c > 1800), "Invalid Hydrotreater Input", ROUND(lh_s * ((sg_f * 1000) / rh_c), 2)))Cracked Cycle-Oil Deep Desulfurization Lower-LHSV Check (Set LHSV = 0.80 hr^-1)
Tighten Design_LHSV B4 from 1.50 down to 0.80 hr^-1 to remove sterically hindered dibenzothiophenes for 10 ppmw ULSD: Required Catalyst Volume E2 jumps to 150.00 m³ (112.50 metric tons in E3), True WHSV E4 drops to 0.91 hr^-1, and Space Time E5 extends to 75.00 min!
=IF(ISTEXT(E4), E4, ROUND(((B2 / B4) * B5) / 1000, 2))Try the example
Use the original values or change them to test your understanding.