Vapor Removal and Pressure Control

Reference ID: MET-792A | Process Engineering Reference Sheets Calculation Guide

Introduction & Context

Vapor removal and pressure control are critical operations in process engineering, particularly within vacuum evaporation systems. The primary objective is to maintain a stable vacuum environment to lower the boiling point of process fluids, thereby protecting heat‑sensitive materials and improving energy efficiency. This calculation suite is used to size essential infrastructure, including condensers, barometric legs, and vacuum extraction equipment (pumps or ejectors). Proper sizing ensures that non‑condensable gases are effectively removed, the latent heat of the vapor is rejected, and the system remains protected against backflow or flooding; for detailed guidance on maintaining the required suction conditions, see our column pressure control methodology.

Methodology & Formulas

The engineering logic follows a sequential approach to determine the thermal load, cooling requirements, hydrostatic head, and gas extraction capacity.

1. Condenser Heat Load: The total heat duty is determined by the mass flow rate of the vapor and its latent heat of vaporization.

\[ Q = \dot{m}_{v} \cdot \lambda \]

2. Cooling Water Flow: The required mass flow rate of cooling water is derived from the heat duty and the allowable temperature rise across the condenser.

\[ \dot{m}_{cw} = \frac{Q}{c_{p} \cdot (T_{out} - T_{in})} \]

Barometric Leg Height: The minimum height required to prevent atmospheric pressure from forcing condensate back into the vacuum vessel is calculated using the hydrostatic pressure balance, and detailed design guidance can be found in the barometric leg for vacuum condenser guide.

\[ z_{min} = \frac{(P_{atm} - P_{vac}) \cdot 1000}{\rho_{water} \cdot g} \]

4. Non-Condensable Gas Removal: The volumetric flow rate of air at suction conditions is determined using the ideal gas law, accounting for the mass fraction of air in the vapor stream.

\[ \dot{V}_{air} = \frac{\dot{m}_{air} \cdot R \cdot T_{abs}}{M_{air} \cdot P_{vac} \cdot 1000} \]

5. Ejector Compression Ratio: The performance requirement for a vacuum ejector is defined by the ratio of discharge pressure to suction pressure.

\[ CR = \frac{P_{atm}}{P_{vac}} \]

Parameter	Constraint / Regime	Threshold
Condensation Feasibility	Thermal Gradient	\(T_{out} < T_{sat}\)
Cooling Water Ratio	Empirical Efficiency	\(20 \leq \frac{\dot{m}_{cw}}{\dot{m}_{v}} \leq 40\)
Barometric Leg	Practical Limit	\(z_{min} \leq 12 \text{ m}\)
Vacuum Pump	Safety Margin	\(Capacity \geq 1.5 \cdot \dot{V}_{air}\)

To establish the correct vacuum setpoint, process engineers should evaluate the following parameters:

Identify the vapor pressure of the process fluid at the maximum allowable operating temperature.
Account for the pressure drop across the piping and vapor recovery equipment.
Ensure the setpoint provides a sufficient safety margin to prevent cavitation in downstream pumps.
Verify that the pressure level does not exceed the structural design limits of the vessel.

Monitoring for system degradation is critical for maintaining process stability. Look for these common indicators:

Gradual increase in vessel pressure despite constant vacuum pump operation.
Excessive vibration or unusual noise coming from the vacuum pump or blower.
Increased power consumption or motor current draw.
Frequent cycling of the pressure control valve or vacuum break system.

Liquid carryover can cause catastrophic failure in vapor removal equipment. Implement these protective measures:

Install a high-efficiency knockout drum or vapor-liquid separator upstream of the pump.
Utilize a mist eliminator pad to capture fine droplets.
Incorporate a high-level switch in the separator to trigger an automatic shutdown of the vacuum source.
Ensure the suction line is sloped toward the separator to prevent liquid pooling.

Worked Example: Condenser and Vacuum System Sizing

A vacuum evaporator processes 5000 kg/h of water vapor at an absolute condenser pressure of 20 kPa, corresponding to a saturation temperature of 60 °C. Cooling water is available at 15 °C, with a target outlet temperature of 35 °C to maintain condensation. Atmospheric pressure is 101.325 kPa. Non-condensable gases (air) are expected to be 2 % of the vapor mass flow. The objective is to determine the cooling water flow rate, barometric leg height, and vacuum pump capacity required to maintain the vacuum.

Known Parameters

Vapor mass flow: \(\dot{m}_{v} = 5000\) kg/h
Condenser pressure: \(P_{vac} = 20\) kPa
Saturation temperature: \(T_{sat} = 60\) °C
Latent heat of vaporization: \(\lambda = 2358\) kJ/kg
Cooling water inlet temperature: \(T_{in} = 15\) °C
Cooling water outlet temperature: \(T_{out} = 35\) °C
Atmospheric pressure: \(P_{atm} = 101.325\) kPa
Non-condensable mass fraction: \(f_{air} = 0.02\)
Gravity: \(g = 9.81\) m/s²
Specific heat of water: \(c_{p} = 4.18\) kJ/(kg·K)
Water density at 60 °C: \(\rho = 983\) kg/m³
Universal gas constant: \(R = 8314\) J/(kmol·K)
Molar mass of air: \(M_{air} = 29\) kg/kmol

Step-by-Step Calculation

Condenser Heat Load
Convert vapor flow to kg/s: \(\dot{m}_{v} = \frac{5000}{3600} = 1.389\) kg/s.
Heat load: \[ Q = \dot{m}_{v} \cdot \lambda = 1.389 \cdot 2358 = 3275.0 \text{ kW} \]
Cooling Water Flow Rate
Temperature rise: \(\Delta T = T_{out} - T_{in} = 35 - 15 = 20\) °C.
Mass flow: \[ \dot{m}_{cw} = \frac{Q}{c_{p} \cdot \Delta T} = \frac{3275.0}{4.18 \cdot 20} = 39.177 \text{ kg/s} \]
Convert to kg/h: \[ \dot{m}_{cw} = 39.177 \cdot 3600 = 141\,037 \text{ kg/h} \]
Cooling water ratio: \[ r_{cw} = \frac{\dot{m}_{cw}}{\dot{m}_{v}} = \frac{141\,037}{5000} = 28.207 \] (within the empirical range of 20–40).
Barometric Leg Height
Minimum height: \[ z_{min} = \frac{(P_{atm} - P_{vac}) \cdot 1000}{\rho \cdot g} = \frac{(101.325 - 20) \cdot 1000}{983 \cdot 9.81} = 8.433 \text{ m} \]
Design height (with 1 m safety margin): \[ z_{design} = z_{min} + 1.0 = 8.433 + 1.0 = 9.433 \text{ m} \]
Non-Condensable Gas (Air) Removal
Air mass flow: \[ \dot{m}_{air} = \dot{m}_{v} \cdot f_{air} = 5000 \cdot 0.02 = 100.0 \text{ kg/h} \]
Convert to kg/s: \[ \dot{m}_{air} = \frac{100.0}{3600} = 0.02778 \text{ kg/s} \]
Absolute temperature: \(T_{abs} = T_{sat} + 273.15 = 60 + 273.15 = 333.15\) K.
Volumetric flow at suction conditions: \[ \dot{V}_{air} = \frac{\dot{m}_{air} \cdot R \cdot T_{abs}}{M_{air} \cdot P_{vac} \cdot 1000} = \frac{0.02778 \cdot 8314 \cdot 333.15}{29 \cdot 20 \cdot 1000} = 0.1327 \text{ m}^3\text{/s} \]
Convert to m³/h: \[ \dot{V}_{air} = 0.1327 \cdot 3600 = 477.6 \text{ m}^3\text{/h} \]
Vacuum pump capacity (with 50 % margin): \[ V_{pump} = 477.6 \cdot 1.5 = 716.4 \text{ m}^3\text{/h} \]
Ejector Compression Ratio and Steam Demand
Compression ratio: \[ CR = \frac{P_{atm}}{P_{vac}} = \frac{101.325}{20} = 5.066 \] (indicating a single-stage ejector is feasible).
Steam demand (mid-range estimate): \[ \dot{m}_{steam} = \dot{m}_{air} \cdot 1.25 = 100.0 \cdot 1.25 = 125.0 \text{ kg/h} \]

Final Summary of Results

Condenser heat load: \(Q = 3275.0\) kW
Cooling water flow: \(\dot{m}_{cw} = 39.177\) kg/s (141 037 kg/h)
Cooling water ratio: \(r_{cw} = 28.207\)
Barometric leg height (minimum): \(z_{min} = 8.433\) m
Barometric leg height (design): \(z_{design} = 9.433\) m
Non-condensable air flow: \(\dot{m}_{air} = 100.0\) kg/h
Volumetric air flow at suction: \(\dot{V}_{air} = 0.1327\) m³/s (477.6 m³/h)
Vacuum pump capacity: \(V_{pump} = 716.4\) m³/h
Ejector compression ratio: \(CR = 5.066\)
Steam demand: \(\dot{m}_{steam} = 125.0\) kg/h

"Un projet n'est jamais trop grand s'il est bien conçu." — André Citroën

"La difficulté attire l'homme de caractère, car c'est en l'étreignant qu'il se réalise." — Charles de Gaulle