Gas Scrubber Design & Sizing: Theory, Demister Mechanics & Equations

1. Process Function: Scrubber vs. KO Drum vs. Filter Separator

A Gas Scrubber (often termed a high-efficiency demisting scrubber or suction scrubber) is an engineered vertical vessel designed to remove fine liquid aerosols and solid particulates from gas streams. While a knock-out drum relies purely on open gravity settling to capture large droplets ($\ge 300\text{--}600\,\mu\text{m}$), a gas scrubber incorporates specialized internal separation equipment—most commonly knitted wire mesh pads, vane-pack mist eliminators, or multi-cyclone bundles—to capture droplets down to $8\text{--}10\,\mu\text{m}$ with greater than 99.5% separation efficiency.

2. Droplet Capture Mechanisms in Demister Internals

The separation of micron-scale droplets within a scrubber's internal packing relies on three distinct physical mechanisms:

1. Inertial Impaction (Dominant for $d_p > 3\text{--}5\,\mu\text{m}$):

   As the gas stream snakes through tightly woven wire filaments or serpentine vane blades, the gas streamlines bend abruptly. Droplets possessing high momentum cannot follow the rapidly curving streamlines and collide with the target wire surface. The efficiency of impaction is characterized by the dimensionless Stokes number:

   $$Stk = \frac{\rho_l d_p^2 v_{gas}}{18 \mu_g d_w}$$

   where $d_w$ is the target wire diameter. When $Stk > 1$, droplet trajectories deviate from streamlines and impact the collector wire.

2. Direct Interception (Dominant for $1\,\mu\text{m} < d_p < 5\,\mu\text{m}$):

   Droplets following the streamline pass within a distance equal to their radius ($r_p = d_p / 2$) from the collector wire surface, touching and coalescing with the liquid film.

3. Brownian Diffusion (Dominant for sub-micron aerosols $d_p < 0.5\,\mu\text{m}$):

   Extremely fine droplets exhibit random thermal molecular bombardment (Brownian motion), causing them to wander across gas streamlines and contact fiber surfaces. High-density candle filters utilize diffusion to achieve 99.9% capture of sub-micron oil mists.

3. Souders-Brown Capacity & Demister Sizing

The cross-sectional area of a vertical scrubber is determined by the maximum allowable gas velocity through the mist extractor to prevent re-entrainment. At high gas velocities, liquid that has coalesced inside the mesh pad is sheared off the top surface and re-atomized into the discharge gas.

The maximum superficial gas velocity is governed by the Souders-Brown equation:

3.1 Mist Extractor Technology Comparison

3.2 GPSA Section 7 Pressure Derating

At operating pressures exceeding atmospheric ($P > 7\,\text{bar a}$), gas density increases, reducing interfacial surface tension forces that anchor coalesced liquid droplets to the mesh wires. The Gas Processors Suppliers Association (GPSA) mandates derating $K_{SB}$ as a function of operating pressure:

In metric units ($P$ in $\text{bar gauge}$):

For operating pressures above 70 bar g (1000 psig), standard mesh pads can lose up to 30–40% of their effective capacity, requiring larger vessel diameters or switching to vane-axial cyclonic separators.

4. Complete Vertical Vessel Height Hierarchy

The total height ($H_{T-T}$, tangent-to-tangent) of a vertical scrubber is constructed from standard engineering zones defined by API Specification 12J and GPSA Section 7:

1. Sump Zone ($H_{LLL}$): Distance from bottom tangent line (BTL) to Low Liquid Level (LLL). Typically $250\text{--}400\,\text{mm}$ to prevent vortex formation into the liquid drain nozzle.
2. Surge / Retention Zone ($H_{LLL}$ to $H_{HLL}$): Liquid volume providing required holdup time ($t_h$):
   • Compressor suction scrubbers: 3 to 5 minutes of peak liquid inflow between normal and high liquid levels.
   • Plant trip volume ($H_{HLL}$ to $H_{HHLL}$): 1 to 2 minutes of surge time to allow automated shutdown before liquid reaches the gas outlet.
3. Inlet Disengagement Zone ($H_{inlet}$): Distance from High-High Liquid Level (HHLL) to inlet nozzle center. Minimum $1.0 \times D_{inlet}$ or $300\,\text{mm}$.
4. Primary Gravity Dropout Space: Distance from top of inlet nozzle to bottom of demister pad. Minimum $600\text{--}900\,\text{mm}$ ($24\text{--}36\,\text{in}$) or $0.75 \times D_v$. This allows primary bulk liquid droplets to drop out before loading the mesh pad.
5. Demister Thickness: Standard mesh pad is $100\text{--}150\,\text{mm}$ ($4\text{--}6\,\text{in}$) thick, supported by grid bars.
6. Disengagement Head Space: Distance from top of demister pad to top tangent line (TTL). Minimum $300\text{--}450\,\text{mm}$ ($12\text{--}18\,\text{in}$) to ensure uniform gas convergence into the vapor outlet nozzle.

5. Inlet Momentum Control & Feed Devices

To avoid bulk liquid shearing at the inlet, the feed nozzle momentum flux must comply with API/Norsok criteria:

A properly selected Schoepentoeter inlet device gently decelerates the two-phase mixture, shaving off up to 80% of bulk liquid into the lower sump before the gas ascends toward the mesh pad.

6. Step-by-Step Worked Sizing Example (Suction Scrubber)

Size a compressor suction gas scrubber operating under the following process conditions:

• Gas mass flow rate: $W_g = 65{,}000\,\text{kg/h}$ ($18.06\,\text{kg/s}$)
• Gas density at $P = 35.0\,\text{bar a}$, $T = 30^\circ\text{C}$: $\rho_g = 28.5\,\text{kg/m}^3$
• Liquid condensate density: $\rho_l = 740\,\text{kg/m}^3$
• Gas viscosity: $\mu_g = 1.35 \times 10^{-5}\,\text{Pa}\cdot\text{s}$
• Liquid entrainment rate: $Q_l = 4.2\,\text{m}^3\text{/h}$ ($0.00117\,\text{m}^3\text{/s}$)
• Required liquid retention time ($NLL$ to $HLL$): $t_h = 5\,\text{minutes}$
• Demister selection: Stainless steel mesh pad ($150\,\text{mm}$ thickness, base $K_0 = 0.107\,\text{m/s}$)

Step 1: Calculate Pressure-Derated $K$-Factor

Operating pressure is $P = 35.0\,\text{bar a} = 34.0\,\text{bar g} = 493.1\,\text{psig}$.

Step 2: Calculate Maximum Allowable Gas Velocity

For design conservatism and turndown margin, select design velocity at 85% of $v_{max}$:

Step 3: Calculate Required Scrubber Internal Diameter

Volumetric gas flow rate:

Required cross-sectional area:

Vessel inside diameter ($D_v$):

Select standard nominal shell internal diameter: $D_v = 1400\,\text{mm}$ ($1.40\,\text{m}$ / 55 in).

Actual cross-sectional area: $A_{actual} = \frac{\pi}{4}(1.40)^2 = 1.539\,\text{m}^2$.

Actual operating velocity: $v_{act} = \frac{0.6337}{1.539} = 0.4117\,\text{m/s}$ (78% of $v_{max}$, optimal operating window).

Step 4: Calculate Liquid Level Heights

Required surge volume for 5 minutes holdup:

Height between NLL and HLL:

Adding standard zones:

• Bottom tangent to LLL ($H_{LLL}$): $300\,\text{mm}$
• LLL to NLL (alarm buffer): $150\,\text{mm}$
• NLL to HLL ($H_{surge}$): $230\,\text{mm}$
• HLL to HHLL (shutdown margin, 2 min): $100\,\text{mm}$
• HHLL to inlet nozzle center: $300\,\text{mm}$
• Inlet nozzle to bottom of demister: $900\,\text{mm}$ (primary disengagement)
• Demister pad thickness: $150\,\text{mm}$
• Demister top to top tangent (TTL): $400\,\text{mm}$

Total Tangent-to-Tangent Height ($H_{T-T}$):

Slenderness aspect ratio: $H_{T-T} / D_v = 2.53 / 1.40 = 1.81$ (ideal for vertical pressure vessels).

7. Operational Troubleshooting & Differential Pressure Monitoring

8. ChemProCal Integration

Perform complete scrubber verification using ChemProCal calculation modules:

• Gas Scrubber Design Calculator: Complete sizing with GPSA pressure derating and internal pad selection.
• Vertical Separator Sizing Tool: Comprehensive droplet settling and nozzle momentum analysis.
• Compressor Power & Sizing Calculator: Size the downstream rotating equipment protected by your scrubber.