SOP: Calculation of Process Time by the Formula Method — Broken Heating Curve

GIFSQ — Global Institute for Food Safety & Quality

Principle

Products such as thick soups, mixed vegetables, syrup-packed sweet potatoes and cream-style corn exhibit broken heating curves — a definite shift from initial convection heating to conduction heating during the process, giving two straight-line portions after the initial lag. The process time is calculated with the second slope f₂ and the break-point values g_bh and x_bh; the lethality during cooling is corrected empirically when the cooling-curve slope f꜀ deviates from the heating slopes.

Materials required

• Heat penetration data showing a consistent break at the same place (the data for one set of conditions must not be used for another)
• Semi-log paper; Fig. 25.21 of the book (r_bh versus log g_bh relationship)
• Table 25-20 (g values from fₕ/U) and Table 25-21 (Fᵣ values) of the book

Procedure — Determination of Bₚ

Note x_bh (time from the beginning of the process to the point of break in the heating curve) and read f_h (first slope) and f₂ (second slope) from the heating curve

↓

Calculate g_bh (the temperature deficit g at which the curve suffers the change in slope) from:

  x_bh

log g_bh = log jI − —————
f_h

Note: the printed layout of this equation is garbled in the available copy; the form above is reconstructed from the book’s symbols, and should be checked against the printed book.

↓

Find r_bh (the proportionality factor corresponding to g_bh) from Fig. 25.21; find Fᵣ corresponding to the retort temperature (Fᵣ = antilog((250 − RT)/z), or from Table 25-21); find f_h/U_bh corresponding to g_bh from Table 25-20

↓

Calculate f₂/U_h2 from the book’s expression (using g_h2, the g value at the end of the heating curve, with r_bh, Fᵣ and f_h/U_bh found above); from this value find the corresponding g_h2 from Table 25-20 — the worked calculations are shown in the book’s Problem 4

↓

Calculate the process time:

Bₚ = f_h·log(jI) + (f₂ − f_h)·log(g_bh) − f₂·log(g_h2)

Note: the printed layout of this equation is garbled in the available copy; the form above is reconstructed from the book’s worked Problem 4 layout, and should be checked against the printed book.

↓

When f꜀ = f₂, calculate Bₚ without the cooling correction, as in the book’s Problem 4 column 17; when f꜀ = f_h, correct log g_h2 by subtracting 0.07(1 − f꜀/f₂) when calculating the process time Bₚ (the correction is added when calculating the sterilizing value F)

Procedure — Determination of F for a broken heating curve

Calculate g_bh from the expression above and find f_h/U_bh from Table 25-20

↓

Calculate g_h2 from the book’s expression and find f_h/U_h2 from Table 25-20; find r_bh corresponding to g_bh from Fig. 25.21

↓

Calculate the sterilizing value using the book’s formula for broken heating curves (illustrated in Problem 5); apply the cooling correction to log g_h2 by adding 0.07(1 − f꜀/f₂)

Note: the printed layout of this F formula is garbled in the available copy and is carried here only as referenced from the worked Problem 5 — it must be verified against the printed book before use.

Precautions

• For want of a precise method of evaluation, products with broken heating curves are treated as if heated by convection; the formula method must be employed with great caution where the heating curve shows only one break.
• The lethality during the cooling phase is taken into account in the formulae by assuming f꜀ = f_h for products without a broken heating curve and f꜀ = f₂ for broken heating curves; where initial cooling occurs by fast convection, a correction to the cooling phase is required as described above.

References

Ranganna, S., Handbook of Analysis and Quality Control for Fruit and Vegetable Products, 2nd edition.

Ball, C.O. & F.C.W. Olson, Sterilization in Food Technology, McGraw-Hill Book Co., New York (1957) — cited in the book.