Packed Column Height for HCl Fume Scrubbing ·

Table of Contents

Vents from hydrochloric acid ($\text{HCl}$) storage tanks present a significant safety and environmental hazard. During filling operations or due to thermal breathing, these tanks can release highly corrosive $\text{HCl}$ fumes. A common solution is a packed column scrubber, but how do you determine the required length or height of the packing?

This post outlines the fundamental engineering calculation for estimating the packed column height ($Z$) needed to scrub $\text{HCl}$ fumes, specifically considering the challenges of a recirculating water system in hot ambient environment like Pakistan.

The Core Equation: HTU & NTU #

The total height of packing ($Z$) required for a specific separation is a product of two key factors:

$$Z = NTU \times HTU$$

NTU (Number of Transfer Units): This represents the difficulty of the separation. It’s a measure of how many “stages” are needed to get from the high inlet concentration to the low outlet target. It is heavily dependent on the driving force (the concentration gradient).
HTU (Height of a Transfer Unit): This represents the efficiency of the packing. It’s a physical characteristic of the packing material (e.g., Pall rings, Raschig rings) and the system’s flow rates. It defines how much packing height is required to achieve one “stage” (one transfer unit).

Our goal is to find $Z$. To do this, we must first find $NTU$ and $HTU$.

Step 1: Design Basis & Ambient Conditions #

Before any calculation, we must define our problem.

Gas: Air and $\text{HCl}$ fumes from a storage tank.
Scrubbing Liquid: Recirculating water.
Location: This is critical. The region can have summer high temperatures of $30^\circ\text{C}$ to $35^\circ\text{C}$ ($303\text{ K}$ to $308\text{ K}$). This high ambient temperature will warm the recirculating water, which dramatically reduces scrubbing efficiency.
Pressure: We assume atmospheric pressure, $P_T \approx 101.3 \text{ kPa}$.

Let’s assume the following for our example:

Inlet Fume Concentration ($y_{in}$): Fumes venting from a $37\% \text{ HCl}$ tank at $30^\circ\text{C}$. The vapor pressure of $\text{HCl}$ in this state is very high, $\approx 240 \text{ mbar}$. $y_{in} = \frac{240 \text{ mbar}}{1013 \text{ mbar}} \approx 0.237$ (or $23.7\%$ by mole)
Target Outlet Concentration ($y_{out}$): We need $99\%$ removal efficiency. $y_{out} = y_{in} \times (1 - 0.99) = 0.237 \times 0.01 = 0.00237$ (or 2370 ppm)

Step 2: Calculating NTU (The “Difficulty”) #

The $NTU$ is calculated by integrating the change in concentration over the driving force. The driving force is the difference between the $\text{HCl}$ in the gas ($y$) and the $\text{HCl}$ that would be in equilibrium with the liquid ($y^*$).

$$NTU = \int_{y_{out}}^{y_{in}} \frac{dy}{y - y^*}$$

Hydrochloric acid is extremely soluble in water. If we use fresh water (not recirculated), the HCl concentration in the water is near zero. This means the equilibrium partial pressure ($y^*$) is also near zero.

For $y^* \approx 0$, the integral simplifies to:

$$NTU \approx \ln\left(\frac{y_{in}}{y_{out}}\right)$$

Using our assumed values: $$NTU = \ln\left(\frac{0.237}{0.00237}\right) = \ln(100) = 4.61$$

So, we need approximately 4.6 transfer units to achieve $99\%$ removal if we use fresh water.

Step 3: Estimating HTU (The “Efficiency”) #

The $HTU$ (Height of a Transfer Unit) is much harder to calculate from scratch. It depends on the gas velocity, liquid loading, packing type, and mass transfer coefficients ($K_G a$).

$$HTU = \frac{G}{K_G a \cdot P_T}$$

Where:

$G$ = Gas molar flux ($\text{mol/s}\cdot\text{m}^2$)
$K_G a$ = Volumetric mass transfer coefficient ($\text{mol/s}\cdot\text{m}^3\cdot\text{Pa}$)

In practice, this value is often provided by the packing vendor or taken from empirical data. For common HCl scrubbing systems with 1-2 inch packing, a typical $HTU$ is often in the range of 0.4 to 0.8 meters.

For our example, let’s assume a reasonably efficient packing: $HTU \approx 0.5 \text{ m}$

Step 4: Final Packed Height Calculation ($Z$) #

Now we can calculate the total packing height:

$$Z = NTU \times HTU = 4.61 \times 0.5 \text{ m} = 2.3 \text{ m}$$

This suggests that 2.3 meters (approx. 7.5 feet) of packing is required for $99\%$ scrubbing under our initial assumptions.

🚨 WARNING: The Problem with Recirculating Water #

Our calculation for $NTU$ made a huge assumption: that $y^* \approx 0$. This is only true for fresh, cold water. You are using recirculating water.

This changes everything.

1. The Heat of Absorption #

The absorption of $\text{HCl}$ into water is extremely exothermic (it generates a lot of heat).

HCl_g ➝ H⁺_(aq) + Cl^-_(aq) $\quad \Delta H_{\text{soln}} \approx -75 \text{ kJ/mol}$

This heat will build up in your recirculating water. In a hot climate ($30-35^\circ\text{C}$ ambient), this water will get very hot, very fast.

2. The Recirculation Saturation #

As the water recirculates, it becomes a dilute acid. As the concentration of HCl in the water ($x$) increases, the equilibrium partial pressure ($y^*$) is no longer zero.

This is the most important concept:

As the water temperature ($T$) increases, $y^*$ increases.
As the water acid concentration ($x$) increases, $y^*$ increases.

The driving force for your scrubber is $(y - y^*)$.

As $y^*$ rises, your driving force collapses. The denominator in the $NTU$ integral gets tiny, and the required $NTU$ skyrockets to infinity.

Your 2.3-meter column will stop working.

The Real-World Solution #

For a recirculating system to work, you must manage the water:

Install a Cooler: The recirculation loop must have a heat exchanger to remove the heat of absorption and keep the water cold. Cold water is a much better solvent.
Use Blowdown/Makeup: You must continuously bleed (blowdown) a portion of the concentrated acid-water and add (makeup) fresh water. This keeps the liquid concentration ($x$) low, which keeps $y^*$ low and maintains the driving force.

The true design calculation must use the full log-mean formula for $NTU$ based on the maximum allowed acid concentration in your recirculating water. But as a first estimate, our 2.3-meter calculation shows what’s possible before heat and saturation take over.