Worked Example: Sizing a Molecular Sieve Dehydration Unit for Cryogenic LNG Feed Drying (< 0.1 ppmv)

Deep cryogenic natural gas processing—such as turboexpander NGL extraction ($-85^\circ\text{C}$ to $-105^\circ\text{C}$) and baseload Liquefied Natural Gas (LNG) liquefaction ($-162^\circ\text{C}$)—mandates feed gas moisture levels below $0.1\text{ ppmv}$ ($< 0.005\text{ lb/MMSCF}$). At these extreme temperatures, residual moisture freezes into solid ice crystals within brazed aluminum plate-fin heat exchangers (cold boxes) and turboexpander nozzles, causing catastrophic differential pressure spikes and plant trips.

This worked example presents the complete process engineering design and equipment sizing for a 2-bed Type 4A molecular sieve dehydration unit treating $10.0\text{ MMSCFD}$ at $60.0\text{ barg}$, detailing water mass balance, zeolite inventory, vessel diameter, Ergun pressure drop, and regeneration thermal balances.

1. Design Basis & Operating Parameters

A front-end engineering design (FEED) study for an LNG feed gas pre-treatment unit defines the following parameters:

Inlet Feed Gas Conditions:

• Gas Flow Rate ($Q$): $10.0\text{ MMSCFD}$ ($11,798.7\text{ Sm}^3/\text{h}$)
• Operating Pressure ($P$): $60.0\text{ barg}$ ($61.01\text{ bar(a)} = 884.9\text{ psia}$)
• Inlet Temperature ($T$): $30.0^\circ\text{C}$ ($86.0^\circ\text{F} = 303.15\text{ K}$)
• Gas Specific Gravity ($G$): $0.65$ ($\text{MW} = 18.83\text{ kg/kmol}$)
• Gas Compressibility ($Z$): $0.862$
• Gas Density ($\rho_g$): $57.2\text{ kg/m}^3$ ($3.571\text{ lb/ft}^3$)

Adsorption System Parameters:

• System Architecture: 2-Bed System (1 Bed Drying / 1 Bed Regenerating & Cooling)
• Adsorption Cycle Time ($t_{cycle}$): $8.0\text{ hours}$
• Desiccant Selected: Type 4A Synthetic Zeolite (Sodium Aluminosilicate, $4.0\text{ \AA}$ pore)
• Pellet Geometry: $1/8\text{"}$ (3.2 mm) spherical beads ($\epsilon = 0.38$)
• Desiccant Bulk Density ($\rho_b$): $720.0\text{ kg/m}^3$ ($45.0\text{ lb/ft}^3$)
• Target Water Specification: $\mathbf{\le 0.1\text{ ppmv}}$ ($-100^\circ\text{C}$ atmospheric dew point)
• Regeneration Temperature ($T_{reg}$): $260.0^\circ\text{C}$ ($500.0^\circ\text{F}$)

2. Step 1: Water Balance & Adsorption Mass Load

A. Inlet Gas Water Content ($W_{in}$):

From the Bukacek correlation for sweet natural gas at $60.0\text{ barg}$ and $30.0^\circ\text{C}$:

$$W_{in} = \mathbf{68.01\text{ lb/MMSCF}} \quad (\mathbf{1,089.4\text{ mg/Sm}^3})$$

B. Hourly and Cycle Water Removal Load:

For $10.0\text{ MMSCFD}$ throughput:

$$\dot{m}_{water,h} = \frac{10.0\text{ MMSCFD} \times 68.01\text{ lb/MMSCF}}{24\text{ h}} = \mathbf{28.34\text{ lb/h}} \quad (\mathbf{12.85\text{ kg/h}})$$

Over an $8.0\text{-hour}$ drying cycle:

$$W_{cycle} = 28.34\text{ lb/h} \times 8.0\text{ h} = \mathbf{226.7\text{ lb H}_2\text{O}} \quad (\mathbf{102.8\text{ kg H}_2\text{O}})$$

3. Step 2: Desiccant Inventory & Bed Volume

Fresh Type 4A molecular sieve exhibits an equilibrium water capacity of $\approx 20\text{ wt}\%$. Per GPSA Figure 20-71, the design useful capacity ($\Delta q$) is derated for hydrothermal aging (3-year lifecycle) and mass transfer zone (MTZ) effects:

$$\Delta q_{design} = 13.0\text{ wt}\% \times 0.79 = \mathbf{10.28\text{ wt}\%} \quad (10.28\text{ lb H}_2\text{O / 100 lb sieve})$$

Required Desiccant Mass per Bed:

$$M_{sieve} = \frac{W_{cycle}}{\Delta q_{design}} = \frac{226.7\text{ lb}}{0.1028} = \mathbf{2,205.0\text{ lb}} \quad (\mathbf{1,000.2\text{ kg}})$$

Total desiccant inventory for two beds $= \mathbf{4,410\text{ lb}}$ ($2,000\text{ kg}$).

Packed Bed Volume:

$$V_{bed} = \frac{M_{sieve}}{\rho_b} = \frac{1,000.2\text{ kg}}{720.0\text{ kg/m}^3} = \mathbf{1.389\text{ m}^3} \quad (\mathbf{49.1\text{ ft}^3})$$

4. Step 3: Vessel Sizing & Superficial Velocity Limits

In downward-flow dehydration service, bed diameter is governed by superficial gas velocity $v_s$ to prevent gas channeling and keep velocity safely below the Ledoux fluidization threshold ($0.35\text{ m/s}$):

Actual Volumetric Gas Flow Rate:

$$Q_{act} = \frac{\dot{m}}{\rho_g} = \frac{10.0 \times 10^6 \times 18.83 / 379.482}{24 \times 3600 \times 57.2} = \mathbf{0.0452\text{ m}^3/\text{s}} \quad (\mathbf{95.8\text{ ACFM}})$$

Selecting Bed Diameter:

Standard vessel sizing selects an inside diameter of $36.0\text{ inches}$ ($0.914\text{ m}$): * Cross-sectional area: $A_{bed} = \frac{\pi}{4} (0.914)^2 = \mathbf{0.6567\text{ m}^2}$ ($7.069\text{ ft}^2$) * Superficial velocity: $$v_s = \frac{0.0452\text{ m}^3/\text{s}}{0.6567\text{ m}^2} = \mathbf{0.069\text{ m/s}} = \mathbf{13.7\text{ ft/min}}$$ (Target design range: $10 - 35\text{ ft/min}$ — Safe from fluidization)

Bed Height & Aspect Ratio:

$$L_{bed} = \frac{V_{bed}}{A_{bed}} = \frac{1.389\text{ m}^3}{0.6567\text{ m}^2} = \mathbf{2.12\text{ m}} \quad (\mathbf{6.94\text{ ft}})$$

Aspect ratio $L/D = \frac{2.12}{0.914} = \mathbf{2.32}$ (GPSA optimal range: $2.0 - 4.0$).

5. Step 4: Ergun Packed Bed Pressure Drop

Pressure drop across clean desiccant beds is calculated via the Ergun equation combining viscous and inertial drag ($\epsilon = 0.38, d_p = 0.0032\text{ m}, \mu = 1.35 \times 10^{-5}\text{ Pa}\cdot\text{s}$):

$$\frac{\Delta P}{L} = 150 \frac{(1 - \epsilon)^2}{\epsilon^3} \frac{\mu v_s}{d_p^2} + 1.75 \frac{1 - \epsilon}{\epsilon^3} \frac{\rho_g v_s^2}{d_p}$$

1. Viscous term: $150 \frac{(0.62)^2}{(0.38)^3} \frac{(1.35 \times 10^{-5})(0.069)}{(0.0032)^2} = \mathbf{95.4\text{ Pa/m}}$
2. Inertial term: $1.75 \frac{0.62}{(0.38)^3} \frac{(57.2)(0.069)^2}{0.0032} = \mathbf{168.3\text{ Pa/m}}$

Total pressure gradient: $$\frac{\Delta P}{L} = 95.4 + 168.3 = \mathbf{263.7\text{ Pa/m}} = \mathbf{0.080\text{ psi/ft}}$$ (GPSA limit: $< 0.33\text{ psi/ft}$ to prevent bed crushing)

Total bed pressure drop: $$\Delta P_{bed} = 263.7\text{ Pa/m} \times 2.12\text{ m} = \mathbf{559\text{ Pa}} = \mathbf{0.038\text{ bar}} \quad (\mathbf{0.55\text{ psi}})$$

6. Step 5: Thermal Regeneration (TSA) Balance

Regeneration is a 3-step cycle: Heating (4.4 hours), Cooling (2.8 hours), and Pressure Equalization (0.8 hours).

Thermal Energy Requirements:

1. Water Desorption Latent Heat ($\Delta H_{des} = 4,186\text{ kJ/kg}$): $$Q_{latent} = 102.8\text{ kg} \times 4,186\text{ kJ/kg} = \mathbf{430,389\text{ kJ}}$$

2. Desiccant Sensible Heat ($C_p = 1.05\text{ kJ/kg}\cdot\text{K}, \Delta T = 230\text{ K}$): $$Q_{des} = 1,000.2\text{ kg} \times 1.05 \times (260 - 30) = \mathbf{241,538\text{ kJ}}$$

3. Vessel Steel Sensible Heat ($M_{steel} \approx 1,400\text{ kg}, C_p = 0.50, \Delta T_{eff} = 161\text{ K}$): $$Q_{steel} = 1,400 \times 0.50 \times 161 = \mathbf{112,718\text{ kJ}}$$

4. Heat Losses (10%): $$Q_{losses} = 0.10 \times (430,389 + 241,538 + 112,718) = \mathbf{78,464\text{ kJ}}$$

Total Regeneration Heat Required: $$Q_{total} = \mathbf{863,109\text{ kJ}} \quad (\mathbf{818.1\text{ MBtu}})$$

Regeneration Heater Duty:

Over $t_{heating} = 4.4\text{ hours}$ ($15,840\text{ seconds}$):

$$\dot{Q}_{heater} = \frac{863,109\text{ kJ}}{15,840\text{ s}} = \mathbf{54.5\text{ kW}} \quad (\mathbf{0.186\text{ MMBtu/h}})$$

Regeneration Gas Flow Rate:

$$\dot{V}_{reg} = \mathbf{370\text{ SCFM}} \quad (\mathbf{5.3\%\text{ of total plant feed}})$$

7. Equipment Sizing Summary