Reference ID: MET-F79A | Process Engineering Reference Sheets Calculation Guide
Introduction & Context
Thermal exhausting is a critical unit operation in the food canning industry, designed to remove air from the headspace of a container prior to hermetic sealing. By heating the product and the headspace, the process induces the expansion of air and the generation of water vapor, which purges the headspace. This is essential for preventing container deformation during subsequent thermal processing, minimizing oxidative degradation of the food product, and ensuring a stable vacuum upon cooling. This calculation is typically employed by process engineers to determine the minimum residence time required in a hot water exhaust box for conduction-dominated food packs.
Methodology & Formulas
The calculation utilizes an empirical transient conduction model. The process assumes that the heat penetration to the cold point of the can follows a first-order thermal response. The required exhausting time is determined by the relationship between the bath temperature, the initial product temperature, and the target temperature required to achieve the desired vacuum.
C: The empirical time constant specific to the product and can geometry (min).
Twater: The temperature of the hot water exhaust bath (°C).
Tinitial: The initial temperature of the product center (°C).
Ttarget: The target center temperature at the time of sealing (°C).
To ensure the mathematical stability of the logarithmic function, the ratio is constrained to prevent division by zero or non-positive logarithmic inputs:
The following table outlines the operational boundaries for this model. If parameters fall outside these ranges, the conduction-based model may be invalid, and alternative heat transfer correlations (such as those for mixing-dominated or forced convection processes) should be applied.
Parameter
Constraint / Condition
Engineering Implication
Bath Temperature
\( 70^\circ C < T_{\text{water}} < 100^\circ C \)
Below 70°C, air removal is inefficient; above 100°C, the model requires pressure correction.
Target Temperature
\( T_{\text{target}} < T_{\text{water}} \)
The product cannot exceed the heating medium temperature.
Exhaust Time (Lower)
\( t_{\text{exhaust}} \geq 5 \text{ min} \)
Values below 5 minutes suggest mixing-dominated heating; model is invalid.
Exhaust Time (Upper)
\( t_{\text{exhaust}} \leq 120 \text{ min} \)
Values above 120 minutes indicate an impractical process for conduction-only heating.
The time constant C is specific to the product formulation, can size, and initial temperature. It must be obtained from heat‑penetration tests where the temperature‑time history at the cold point is recorded and fitted to the first‑order conduction model. Using a generic value without experimental validation will lead to inaccurate exhausting times.
This model assumes operation at atmospheric pressure. If the bath temperature exceeds 100 °C, the water will boil and the heat transfer mechanism changes. A pressurized exhaust box is required, and different heat transfer correlations must be used to account for the altered driving force and possible steam blanketing.
If the calculated exhausting time falls below 5 minutes, the heating is too rapid to be conduction‑dominated. In such cases, forced convection or mixing effects dominate, and the first‑order empirical model would over‑predict the rate of temperature rise, potentially leading to an under‑designed exhausting time and inadequate vacuum.
Worked Example: Thermal Exhausting Time for No. 2 Cans (Solid Pack)
A process engineer must determine the minimum holding time in a hot-water exhaust box for No. 2 cans (307 × 409) filled with a solid pack of carrots in brine. The cans enter the exhaust box at room temperature and must be heated until the product center temperature reaches 82 °C to achieve the desired final vacuum after cooling. The empirical time constant for this product/can combination has been determined from prior heat-penetration tests.
Initial product center temperature, \(T_{\text{initial}} = 25.0\;^{\circ}\text{C}\)
Target product center temperature at sealing, \(T_{\text{target}} = 82.0\;^{\circ}\text{C}\)
Empirical time constant for No. 2 can / solid pack, \(C = 22.0\;\text{min}\)
Step-by-Step Calculation:
Calculate the temperature difference between the bath and the initial product:
\[
T_{\text{water}} - T_{\text{initial}} = 85.0\;^{\circ}\text{C} - 25.0\;^{\circ}\text{C} = 60.0\;^{\circ}\text{C}
\]
Calculate the temperature difference between the bath and the target center temperature:
\[
T_{\text{water}} - T_{\text{target}} = 85.0\;^{\circ}\text{C} - 82.0\;^{\circ}\text{C} = 3.0\;^{\circ}\text{C}
\]
Compute the dimensionless temperature ratio:
\[
\frac{T_{\text{water}} - T_{\text{initial}}}{T_{\text{water}} - T_{\text{target}}} = \frac{60.0}{3.0} = 20.0
\]
Apply the empirical exhaust-time equation:
\[
t_{\text{exhaust}} = C \cdot \ln\!\left( \frac{T_{\text{water}} - T_{\text{initial}}}{T_{\text{water}} - T_{\text{target}}} \right)
\]
Substituting the values:
\[
t_{\text{exhaust}} = 22.0\;\text{min} \cdot \ln(20.0)
\]
Using the natural logarithm of 20.0:
\[
t_{\text{exhaust}} = 65.906\;\text{min}
\]
Validity checks (using the Numerical Results from the calculation engine):
Bath temperature \(85.0\;^{\circ}\text{C}\) lies within the valid range of 70 °C to 100 °C – pass.
Target temperature \(82.0\;^{\circ}\text{C}\) is less than bath temperature \(85.0\;^{\circ}\text{C}\) – pass.
Calculated exhaust time \(65.906\;\text{min}\) is above the 5-minute lower bound for conduction-dominated heating – pass.
Calculated exhaust time is below the 120-minute upper bound considered practical for conduction-only heating – pass.
Final Answer:
The required batch thermal exhausting time for the No. 2 cans of solid-pack carrots in brine is 65.906 minutes (rounded to three decimal places). This corresponds to holding the cans in the 85 °C exhaust bath for approximately 66 minutes before sealing, ensuring the product center reaches the target temperature of 82 °C for the desired final vacuum.
"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
