Mechanical and Thermal Compression Methods

Reference ID: MET-51F5 | Process Engineering Reference Sheets Calculation Guide

Introduction & Context

Steam-jet thermocompression is a critical unit operation in process engineering, particularly within evaporation and distillation systems. By utilizing a steam ejector, low-pressure process vapors are entrained and compressed to a higher pressure using high-velocity motive steam. This process effectively recovers latent heat that would otherwise be rejected to a condenser, significantly improving the energy efficiency of the plant. It is most commonly applied in falling-film evaporators for food processing, chemical concentration, and desalination, where it serves as a cost-effective alternative to mechanical vapor recompression (MVR).

Methodology & Formulas

The performance of a thermocompressor is governed by mass and energy conservation principles within the ejector control volume, and detailed calculations such as the steam‑jet ejector vacuum calculation can be used to determine the achievable vacuum levels. The following formulas define the thermodynamic state of the system:

The compression ratio (R_c) and expansion ratio (R_p) are defined by the operating pressures:

\[ R_{c} = \frac{P_{\text{discharge}}}{P_{\text{suction}}} \] \[ R_{p} = \frac{P_{\text{motive}}}{P_{\text{suction}}} \]

The mass balance for the ejector, based on a unit mass of motive steam, is determined by the entrainment ratio (ω):

\[ \dot{m}_{\text{suction}} = \omega \cdot \dot{m}_{\text{motive}} \] \[ \dot{m}_{\text{discharge}} = \dot{m}_{\text{motive}} + \dot{m}_{\text{suction}} \]

The enthalpy of the discharge stream (h_discharge) is calculated via the energy balance, assuming an adiabatic mixing process where kinetic energy conversion is internal to the ejector:

\[ h_{\text{discharge}} = \frac{(\dot{m}_{\text{motive}} \cdot h_{\text{motive}}) + (\dot{m}_{\text{suction}} \cdot h_{\text{suction}})}{\dot{m}_{\text{discharge}}} \]

The degree of superheat (ΔT_superheat) in the discharge steam is derived from the excess enthalpy relative to the saturated vapor enthalpy (h_g,discharge) at the discharge pressure:

\[ \Delta H = h_{\text{discharge}} - h_{g,\text{discharge}} \] \[ \Delta T_{\text{superheat}} = \frac{\Delta H}{C_{p,\text{steam}}} \]

The overall system performance is quantified by the steam economy (SE):

\[ SE = 1 + \omega \]

Parameter	Condition/Constraint	Limit/Threshold
Compression Ratio (R_c)	Empirical Validity	1.5 ≤ R_c ≤ 8.0
Entrainment Ratio (ω)	High Compression Limit	ω < 1.0 if R_c > 2.5
Suction Pressure (P_suction)	Triple Point Avoidance	P_suction > 0.6 kPa
Discharge State	Thermodynamic Phase	If h_discharge > h_g,discharge, steam is superheated

Mechanical and thermal compression methods serve different operational needs in process engineering:

Mechanical Vapor Compression (MVC) utilizes a motor-driven compressor to increase the pressure and temperature of vapor, making it highly energy-efficient for closed-loop systems.
Thermal Vapor Compression (TVC) uses high-pressure motive steam through an ejector to entrain and compress lower-pressure vapor, which is ideal for facilities with excess steam capacity.

Mechanical compression is generally preferred when the primary goal is energy optimization and electricity costs are favorable compared to steam costs. Consider this method when:

The process requires precise control over the compression ratio.
The facility lacks a reliable or cost-effective supply of high-pressure motive steam.
The system operates with a relatively low temperature lift requirement.

Because TVC systems rely on high-velocity steam flow, maintenance should focus on the integrity of the ejector nozzle and diffuser. Key tasks include:

Regular inspection of the motive nozzle for erosion or scaling that can degrade entrainment efficiency.
Monitoring the motive steam pressure to ensure it remains within the design specification of the ejector.
Checking for internal fouling that may disrupt the flow geometry and reduce the compression ratio.

The suction pressure is critical for preventing compressor surge. To maintain stability:

Ensure the control logic dynamically adjusts the compressor speed based on real-time feedback of the suction pressure.
Implement anti-surge bypass valves to protect the mechanical components during transient process conditions.
Verify that the sensor calibration for the suction pressure is checked periodically to avoid drift in the control loop.

Worked Example: Steam-Jet Thermocompression for Evaporation

Scenario: A falling-film evaporator concentrates fruit juice. A steam-jet thermocompressor entrains low-pressure vapor from the separator to improve thermal efficiency. Given the operating conditions below, calculate the discharge steam condition and the overall steam economy.

Known Parameters

Motive steam mass (basis): \( m_{\text{motive}} = 1.0 \) kg
Motive steam pressure: \( P_{\text{motive}} = 1000.0 \) kPa
Motive steam temperature: \( T_{\text{motive}} = 180.0 \) °C
Motive steam specific enthalpy: \( h_{\text{motive}} = 2778.1 \) kJ/kg
Suction vapor pressure: \( P_{\text{suction}} = 20.0 \) kPa
Suction vapor specific enthalpy: \( h_{\text{suction}} = 2609.0 \) kJ/kg
Discharge pressure: \( P_{\text{discharge}} = 80.0 \) kPa
Saturated vapor enthalpy at discharge: \( h_{g,\text{discharge}} = 2662.0 \) kJ/kg
Entrainment ratio: \( \omega = 0.7 \) kg suction per kg motive
Specific heat of steam: \( c_p = 2.0 \) kJ/(kg·K)

Step-by-Step Calculation

Mass Balance
With a motive mass of 1.0 kg, the entrained suction mass is:
\( m_{\text{suction}} = \omega \cdot m_{\text{motive}} = 0.7 \cdot 1.0 = 0.7 \) kg.
Total discharge mass:
\( m_{\text{discharge}} = m_{\text{motive}} + m_{\text{suction}} = 1.0 + 0.7 = 1.7 \) kg.
Energy Balance
Assuming adiabatic mixing (no heat transfer to surroundings), the discharge specific enthalpy is the weighted average of inlet enthalpies:
\[ h_{\text{discharge}} = \frac{ m_{\text{motive}} \cdot h_{\text{motive}} + m_{\text{suction}} \cdot h_{\text{suction}} }{ m_{\text{discharge}} } \]
Substitute the known values:
\( h_{\text{discharge}} = \frac{1.0 \cdot 2778.1 + 0.7 \cdot 2609.0}{1.7} = 2708.471 \) kJ/kg (rounded to 3 decimals).
Superheat Determination
The discharge enthalpy exceeds the saturated vapor enthalpy at the same pressure. The enthalpy difference is:
\( \Delta h = h_{\text{discharge}} - h_{g,\text{discharge}} = 2708.471 - 2662.0 = 46.471 \) kJ/kg.
Using the specific heat of steam, the resulting superheat temperature is:
\[ \Delta T_{\text{superheat}} = \frac{\Delta h}{c_p} = \frac{46.471}{2.0} = 23.235 \text{ °C}. \]
Thus, the discharge steam is superheated by about 23.235 °C above the saturation temperature at 80 kPa (93.5 °C).
Steam Economy
The steam economy is defined as the total mass evaporated per unit mass of motive steam. For a single-effect evaporator with thermocompression:
\( \text{SE} = 1 + \omega = 1 + 0.7 = 1.7 \).
This means each kilogram of motive steam effectively evaporates 1.7 kg of water from the juice.
Validity Check
The compression ratio \( R_c = P_{\text{discharge}} / P_{\text{suction}} = 4.0 \) lies within the empirical range (1.5 – 8.0). The expansion ratio is \( R_p = P_{\text{motive}} / P_{\text{suction}} = 50.0 \). An entrainment ratio of 0.7 for \( R_c = 4.0 \) is typical for a well-designed multi-element ejector.

Final Answer

The thermocompressor discharge steam has a specific enthalpy of 2708.471 kJ/kg and is superheated by 23.235 °C. The steam economy of the system is 1.7 kg evaporated per kg motive steam.

"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