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Is There a Need for the Come-Up Time Correction Factor in Ball’s Formula Method? A Critical Analysis

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Abstract

A critical analysis of the correction factor for the come-up time (CUT) introduced by Dr. C. Olin Ball in his Formula Method for thermal process calculations is described in this manuscript. In the General Method, the effect of the CUT is included in the calculated lethality value as long as numerical integration is carried out over the entire cold spot temperature–time profile from the point when the steam is turned on. The hypothesis of this communication is that Ball’s Formula Method, just like the General Method, includes the effect of the CUT in its calculations. Ball’s Formula Method utilizes a “curve fitting” of the experimental time–temperature data regardless of where the time zero is placed within the come-up time. Therefore, the effect of the CUT is automatically included, because, as in the General Method, Ball’s Formula Method is fitting and managing experimental data. In addition, the regressed time–temperature data used for lethality calculations are exactly the same independent of the time zero location. To evaluate the rationale of the CUT correction factor, computer-simulated time–temperature data and experimental runs were evaluated with time zero shifted to different locations (100, 70, 42, 20 and 0% of the CUT). In addition, the effect of the CUT (shape and length) was studied in terms of F Heating and T g accuracy compared to the General Method. Independent of the time shift (the location of time zero), the calculations according to the Formula Method for total heating time (P t  + CUT) were always the same. This work states that it is not necessary to shift the location of time zero in Ball’s Formula Method because the calculations over the curve fitting time–temperature data will always include the effect of the CUT regardless of where time zero is placed.

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Fig. 1
Fig. 2

Abbreviations

B :

Ball’s effective processing time

CUT :

Come-up time

F o :

Sterilizing value at 121.1 °C

F p :

Process sterilizing value

F Heating :

Process sterilizing value at the heating stage

f :

Rate factor (related to slope of semi-log heat penetration curve)

f h and f c :

Heating and cooling rate factors (related to slope of semi-log heat penetration curve)

j :

Dimensionless lag factor \( \left( {j = \frac{{{\text{TRT}} - T_{A} }}{{{\text{TRT}} - {\text{IT}}}}} \right) \)

j h and j c :

Heating and cooling lag factors

P t :

Operator’s process time (measured from the time when the retort reaches processing temperature (TRT) until the time when the steam is turned off)

T A :

Extrapolated initial can temperature obtained by linearizing entire heating curve of a can

T g :

Temperature at the coldest point when cooling phase begins

T :

Temperature

IT :

Initial temperature

TRT :

Retort temperature

T ref :

Reference temperature, 121.1 °C

t :

Time

Time zero :

In Ball’s procedure, the location of time zero has been shifted and starts when the time corresponds to 0.58 * CUT (e.g., if the CUT = 10 min, then time zero is located at 5.8 minute of the regular time)

t g :

Time in a thermal process corresponding to heat cut off and initiation of cooling phase

z :

Temperature change necessary to alter the TDT by one log-cycle

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Acknowledgments

We kindly appreciate the contribution made by Dr. Alik Abakarov (Universidad Politécnica de Madrid, Spain). Authors Ricardo Simpson and Sergio Almonacid are grateful for the financial support provided by CONICYT through FONDECYT project number 1090689.

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Authors and Affiliations

  1. Departamento de Ingeniería Química y Ambiental, Universidad Técnica Federico Santa María, P.O. Box 110-V, Valparaíso, Chile

    Ricardo Simpson, Sergio Almonacid, Helena Nuñez & Alejandra Urtubia

  2. Centro Regional de Estudios en Alimentos Saludables (CREAS). CONICYT-REGIONAL. R06I1004, Blanco 1623, Room 1402, Valparaíso, Chile

    Ricardo Simpson, Sergio Almonacid & Alejandra Urtubia

  3. Department of Agricultural and Biological Engineering, University of Florida, Frazier Rogers Hall, P. O. Box 110570, Gainesville, FL, 32611-0570, USA

    Arthur A. Teixeira

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  1. Ricardo Simpson
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  2. Sergio Almonacid
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  3. Helena Nuñez
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  4. Alejandra Urtubia
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  5. Arthur A. Teixeira
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Correspondence to Ricardo Simpson.

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Simpson, R., Almonacid, S., Nuñez, H. et al. Is There a Need for the Come-Up Time Correction Factor in Ball’s Formula Method? A Critical Analysis. Food Eng Rev 4, 107–113 (2012). https://doi.org/10.1007/s12393-012-9049-9

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  • DOI: https://doi.org/10.1007/s12393-012-9049-9

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