11 replies to this topic

[achien]

How to manually calculate B* and C *
if i used retort

[Bawdy]

Hi Achien,

I have no idea by what you mean by C, perhaps some more info?

I also assume that when you are asking how to calculate B you are actually asking for the formula.

B = Process Time + (0.4 x Come Up Time).

NB all time units are minutes

eg Process time of 50 minutes with CUT of 10 minutes

Therefore B = 50 + (0.4 *10)

B=54

Hope that helps.

Paul.

[achien]

B * is describes the reduction of spores thermofilik 10⁹/unit and C * is described the destruction conditions as much as 3% thiamin/unit. both is similar with F0. When we calculate F0, we must validate the F0 value using B* and C*, but i dont know how to calculate manually the B* and C*...Can u help me

[Charles.C]

B * is describes the reduction of spores thermofilik 10⁹/unit and C * is described the destruction conditions as much as 3% thiamin/unit. both is similar with F0. When we calculate F0, we must validate the F0 value using B* and C*, but i dont know how to calculate manually the B* and C*...Can u help me

Dear achien,

I am guessing these are the type of equations you are seeking (?) although i expect Bawdy is more likely to know about their interpretation.

 milk lethality, B and C stars.png   270.5KB   38 downloads

Rgds / Charles.C

added - I note that all these equations require an integration step, eg trapezoidal methods etc in case of F0, is that the "calculation" you are talking about ?

added(2) I assume you appreciate the differential logic of equations in above attachment. Just to spell the requirement a little more clearly, the start calculation (ie integration formula) for B* from basic time/temp.data is given in attachment below. The possible basic methods of integration (eg numerical, graphical) will be similar to those given for Fo as detailed in all the heat process books (some are explained in detail with examples in refs linked in my posts in this thread - http://www.ifsqn.com...dpost__p__48963

 milk lethality, calculation F0, Bstar.png   300.24KB   22 downloads

However Bawdy's suggestion in the post #6 is obviously quicker to apply if you hv some data ??

[Bawdy]

Hi Achien,


I had a quick look at the university of Google, and it appears that the B* and C* values are used for continuous flow thermal processing, an area in which i have no experience unfortunately. Sorry about that.

However in regards to a B* value, for retorting, in still batch retorts, it seems to be irrelevant, as the F0 value will be able to determine if you have delivered sufficient heat to kill the target organism, or reduce it by a set number of logs. Or at least that is my understanding. The B* value is to continuos flow what F0 is to Static retorts.

In all of my years of retorting experience (sealed cans and plastic pots/pouches) we never discussed B values, only F0s.

Out of curiosity, what was the F0 you achieved?

Paul.

[Bawdy]

Hi Achien,

I have just read Charles reply above, whilst i do not understand your process i do understand the maths. If you could tell me what the F0 you achieved in the retort is, plus the D value of the target organism at 121.1 is i could calculate the log reduction. By knowing the number of log reductions you could then compare it to your current B* value log reduction.


To assist you, you may be able to do it also by knowing that F0 is calculated at 121.1 degrees, using C.Botulinum, which has a D value of 0.23 and a Z of 10.

So F0 of 2.8 = a 12 log reduction of C.bot, i.e 2.8/.23 = 12 (or very near to it). If you achieved a F0 of 6, number of log reductions of C.bot = 26.3.

If your target organism has a D value at 121.1 of say 2, then your F0 would need to be 9 (because you are looking for a minimum of a 9 log reduction) x 2 minutes, i.e an F0 of 18 minumum to get the the equivalent of a B* value of 1.

Hope that helps.

Paul.

[achien]

Dear achien,

I am guessing these are the type of equations you are seeking (?) although i expect Bawdy is more likely to know about their interpretation.

 milk lethality, B and C stars.png   270.5KB   38 downloads

Rgds / Charles.C

added - I note that all these equations require an integration step, eg trapezoidal methods etc in case of F0, is that the "calculation" you are talking about ?

added(2) I assume you appreciate the differential logic of equations in above attachment. Just to spell the requirement a little more clearly, the start calculation (ie integration formula) for B* from basic time/temp.data is given in attachment below. The possible basic methods of integration (eg numerical, graphical) will be similar to those given for Fo as detailed in all the heat process books (some are explained in detail with examples in refs linked in my posts in this thread - http://www.ifsqn.com...dpost__p__48963

 milk lethality, calculation F0, Bstar.png   300.24KB   22 downloads

However Bawdy's suggestion in the post #6 is obviously quicker to apply if you hv some data ??

[achien]

Data Logger
No T (Celcius) F0 1 100.5087 0.002922 2 103.8854 0.010841 3 107.5106 0.030546 4 110.8715 0.078996 5 114.3348 0.196472 6 116.7729 0.444548 7 118.5864 0.87162 8 119.865 1.506087 9 120.8853 2.359154 10 121.5721 3.421595 11 122.0551 4.656993 12 122.4452 6.03997 13 121.2379 7.288621 14 117.3833 7.961384 15 112.344 8.180235 16 106.7589 8.236396 17 101.2744 8.24974

[achien]

Dear Mr charles and mr bawdy

That is my data and i get fo is 8,

i just want to proof that our process is good enough so i calculate b* and c*
how about that

Thank you

[Bawdy]

Achien,



From what you have provided i get the following.

B* of 1 = 10.5 secs at 135 degrees. which gives a 9 log reduction.

Therefore D at 135 = 9/10.5 = 0.89sec

using a z of 10.5, the equivalent time at 121.1 to achive a 1 log reduction = 19.7 sec, so to achieve a 9 log reduction at 121.1 = 9 x 19.7 = 178 sec.

Divide 178 by 60, to convert to minutes = 2.96 minutes, which means you need a min F0 of 2.96 to get a b* equivalent of 1. So your value of 8 is well in excess of this.

If you look at Charles attachments above it says that you need to get a F0 of about 3 to achieve safety which fits in perfectly well with my calculated figures above.

Hope that helps, i will try and do the same for the the C* values tomorrow, as i do not have time today. This is also why this post is so brief, have to have a heap of specs finished before the end of today.



Regards,

Paul.

[Tony-C]

Dear Mr charles and mr bawdy

That is my data and i get fo is 8,

i just want to proof that our process is good enough so i calculate b* and c*
how about that

Thank you

Hi there

I can see some of the logic in Paul's calculations but not for the B*

Some background:

F₀ value

The connection between time and temperature of sterilisation is expressed as a F₀ value according to the following logarithmic function:

F₀ = t/60 x 10 ^{(T-121.1˚C/z)}


where

t = sterilisation time in seconds at T °C

T = sterilisation temperature in °C

z = a value expressing the increase in temperature to obtain the same lethal effect in the 1/10 of time. The value varies with the origin of the spores (10 – 10.8°C) and can generally be set as 10°C.

F₀ = 1 for product is heated at 121.1°C for 1 minute.

For milk a F₀ value of minimum 5 – 6 is normally required.

B* and C* values

The effective working range of UHT treatments is defined in some countries by reference to:

Bacteriological effect: B* (known as B star)

Chemical effect: C* (known as C star)

B* is based on the assumption that commercial sterility is achieved at 135°C for 10.1 sec. with a corresponding z value of 10.5°C. This reference process is given a B* value of 1.0, representing a reduction of thermophilic spore count of 10⁹ per unit.

The C* value is based on the conditions for 3% destruction of thiamine per unit. This is equivalent to 135°C for 30.5 seconds with a z value of 31.4°C.

B* = t / 10.1*10 ^{( (T - 135˚C ) / 10.5)}

C* = t / 30.5 * 10 ^{(( T - 135˚C ) /31.4)}


So for a process of 140˚C for 4 seconds where the f0 is about 5.2

B* Calculation for 140 C 4 second hold
t/10.1 = 0.40 140 minus 135 = 5 Z=10.5 Result 1.19

C* Calculation for 140 C 4 second hold
t/30.5 = 0.13 140 minus 135 = 5 Z=31.4 Result 0.19

D Value

When bacteria are subjected to moist heat at lethal temperatures they undergo a logarithmic order of death. The time interval required to bring about one decimal reduction (i.e., a 90% reduction) in the number of survivors.
This time interval is known as the decimal reduction time, or the "D value".
The D value for bacterial spores is independent of initial numbers, however, it is affected by the temperature of the heating medium. The higher the temperature the faster the rate of thermal destruction and the lower the D value.
The unit of measurement for D is "minute" (the temperature is also specified, and in most canning operations it can be assumed to be 121.1°C).

Have a look at the first summary sheet in the attached table.

 Calculation f0 & B & C.xlsx   41.52KB   55 downloads

I have highlighted the line for Clostridium botulinum with a D value of 0.23 used an f0 of 2.8 is required and this is equivalent to a B* of 0.58 and a C* of 0.16

I have highlighted the line for your process and an f0 of 8.24 B* is 1.74 and C* is 0.49

Regards,

Tony

Edited by Tony-C, 25 November 2011 - 02:53 PM.

[Charles.C]

Dear achien,

Regarding yr datalogger results, I assume the “No” = times in minutes, eg the last point is 101.27degC after 17min. If the data is supposed to be seconds and/or other errors, you can repeat calculations below yourself.

Based on above assumed temperatures / times this is presumably not a UHT process, so that the extrapolation to usage of B*,C* is perhaps rather problematic but never mind .

I am not entirely sure of what you are seeking to prove however I hv located an on-line website/calculator program which may help, see –

http://www.dairyscie...info/uht123.asp

(strictly, yr data is not totally appropriate [non-UHT process], however the mathematical procedure should still work if the equation holds / sufficient data points, and the f0 result [albeit at ref.121.1degC] seemed OK so I went ahead anyway.)

With data assumptions as above, the on-line program gave results for F0, B*, C* of approx 8.3, 2.4, 8.1 respectively. Obviously the result for C* is prohibitive.

I enclose a snapshot of procedure/inputs. (there are a few dummy data at start/finish for “testing” since ideally, a “zero” and min. 20 points seem to make the program happy). I also truncated yr datalogger temps to one (unrounded) decimal point.

 procedure for thermal F0, Bstar, Cstar.png   41.13KB   7 downloads

As an example - a calculation for the displayed (“instantaneous”) B* result in B* column at 660sec/122degC uses the formula in previous posts –

(instantaneous B*) = 10 ^((T-135)/10.5) / 10.1

using 122degC gave me approx 0.00578 on hand calculator (cf table value 0.006)
The overall results are (program) obtained via trapezoidal integration. (involves summing individual column results, maybe little more number manipulation/ multiplying by time step [60secs in example])(can be done manually or via Excel sheet, particularly since many points here are "zero", otherwise 'manual" can get rather time-consuming IMEX ) .

From a brief (very not my area) look in the UHT textbooks the present results for B*, C* will inevitably be different to those in previous post (cf. 1.74, 0.49) since the calculation there was for a rather different setup / set of formulae. Or I hv simply wrongly interpreted/inputted the original data, equally possible . No problem to adjust on-line anyway.

I also noticed these picture which seemed to helpfully illustrate the (in-pack)/ (UHT) process significance of limiting values for heating time, B*, C* –

 process visualisation of use of Bstar,Cstar.png   37.86KB   8 downloads
 process visualisation Bstar,Cstar (pic2).png   127.46KB   2 downloads

Rgds / Charles.C