Analysis of sugar attenuation with curve- fitting method

The Science of Beer 1

Analysis of sugar attenuation with curve-fitting method and its application for industrial fermentation control.

Taku Irie and Yoshinori Ito Production Technology Center

Asahi Breweries, Ltd.

ASBC Annual Meeting La Quinta, 17th June, 2015


Contents

• Background

• The purpose of the study

• Curve fitting for industrial scale fermentation

– Method

– Result

– Cases of analysis and process improvement with curve fitting

• Summary


Background : Controlling fermentation in the industrial brewing

• Factors to control fermentation in practical brewing

– At the beginning of the fermentation Pitching Aeration rate Transfer time, interval Wort cooling temperature (=Start temperature) Additives

– During the fermentation Temperature Pressure



• Factors “at the beginning of” the fermentation -We’ve developed various methods and put them to practical use (2,000~5,000 HL).

“Ester control in practice” (Tajika, Brewing Summit 2014) Our technology… - Dual effect of oxygen consumption by yeast (T. Irie, EBC 2009) - Ununiform fermentation (Y. Nakamura & H. Koizumi, WBC 2012) - Amino acid addition to wort (Y. Tajika, Brewing Summit 2014)



• Factors “during” the fermentation - We already have some knowledges “how to do” to control with temperature or pressure.

0.0

5.0

10.0

15.0

20.0

25.0

30.0

Isothermal Process "Cooling in the latter"

Fermentation Pattern

Eth

yl A

ceta

te [p

pm]

Example 1 : “Cooling in the latter” process for ester control

Ref. : “Isothermal Process” 17 ºC 6days Test. : “Cooling th the latter” 17 ºC 3days + 15ºC 3days

To prolong the stationary phase and increase of the period of esterization



• Factors “during” the fermentation …But we need more information about “when to do”.

Example 1: “Cooling in the latter” process for ester control

That should depends on the yeast growth phase…,

but how to find it out?

0 40 80 120 160 200 240 Time [h]

Temperature

Extract Yeast



• Factors “during” the fermentation - We already have some knowledges “how to do” to control with temperature or pressure.

Example 2 : Controlling Sulphury flavour

- Temperature control would be effective for yeast growth.

- Hydrogen sulfide has a peak in the log phase of yeast growth. Knowledge



• Factors “during” the fermentation - We already have some knowledges “how to do” to control with temperature or pressure. …But we need more information about “when to do”.

Example 2 : Controlling Sulphury flavour

- Temperature control would be effective for yeast growth.

- Hydrogen sulfide has a peak in the log phase of yeast growth. Knowledge

For practical brewing

- When should we cool the fermentor on (and off) to suppress the sulphury flavour?


Background : Hypothesis

- How to find out the appropriate time to control? with high reliability… without additional effort…



- How to find out the appropriate time to control? with high reliability… without additional effort…

- ”Information extraction” from daily data.

0.0

5.0

10.0

15.0

0 20 40 60 80 100 120 140 160[h]

Ext

ract

[%P

]

0.0

15.0

30.0

45.0

Yea

st [*

106

cell/

mll]


0.0

5.0

10.0

15.0

0 20 40 60 80 100 120 140 160[h]

Ext

ract

[%P

]

0.0

15.0

30.0

45.0

Yea

st [*

106

cell/

mll]


Log

Pha

se

Sta

tiona

ry

Pha

se

Lag

Pha

se

- Attenuation describes sigmoidal curve and its rate would reflect the number of yeast. - The changing point of the curve would suggest borders between yeast growth phases.


Background

- Curve fitting to apparent extract with sigmoidal function (MacIntosh, ASBC2011)

( ) ( ){ }MtaPPPtP ei

e −−+−

+=exp1

Logistic Curve

AE ’

0 15 30 45 60 75

P i

P e M

B

AE

OE OE 15

12

9

6

3


The Purpose of the study

- In this study, we examined curve-fitting method to analyze the attenuation data in beer fermentation.

- By this method, we tried to obtain information about appropriate time to control fermentation.

- We investigated whether this method would be useful for analyzing and controlling fermentation even in the industrial brewing(2,000~5,000HL).


Methods：Curve fitting with apparent extract

- Least-square method with Solver add-in on Microsoft Excel®

- 4-parameter sigmoid curves

( ){ } dbta

KtP +−+

=exp1

)(Logistic function

( ) daKtP bt +⋅= exp)(

Gompertz function

P : apparent extract [%P], t : fermentation time [h], K,a,b,d : Parameters

0

6.15

12.3

0 50 100 150Time[h]

Atte

nuat

ion

Logistic Gompertz


Methods：Curve fitting with apparent extract

- Least-square method with Solver add-in on Microsoft Excel®

0

6.15

12.3

0 50 100 150Time[h]

Atte

nuat

ion

Logistic Gompertz

R 2̂

0.990

0.992

0.994

0.996

0.998

1.000

Logistic Gompertz

Gompertz shows better fittness.


Local Max. Maximum

Local Min.

0 50 100 150 200Time［h］

Ext

ract

, Con

sum

ptio

n ra

te

Cur

vatu

re

0

Method : Changing points of fitting curve

- Maximum on attenuation rate : Inflexion Point (IP)

- Local extrema on curvature : Curving Points (CP)

IP

Curvature

⋅

+==

−

2

223

2

11dt

yddtdy

Rκ

2nd CP

1st CP

Atte

nuat

ion

and

Rat

e

Cur

vatu

re

Attenuation Rate

dtdyv =


0 20 40 60 80 100 120 140 160 180

Time [h]

Atte

nuat

ion

[%]

Brewery A Brewery B Brewery C Brewery D Brewery E

Result：Fitting curves with changing points

1st Curving point

Inflexion point

2nd Curving point


Short summary

• We could find out the sigmoidal curve which would suit for our attenuation data.

• With this curve we could calculate changing points (Inflexion point and two curving points).

• The position of the points depends on breweries, regardless of brewing for the same brand.


Result : Cases of process improvement with curve fitting

• We put this method into practical use to find out the appropriate time for temperature control to … Case (1) : Decrease sulphury flavour Case (2) : Increase ester aroma


0

1

2

3

4

5

Sco

re o

f "S

ulph

ury"

in s

enso

ry te

st

Brewery F Average of 7 breweries

Example１：Control of sulphury flavour

• Sensory test for monthly sample of Brand X

- Brewery F had higher score in sulphury flavour.


0 20 40 60 80 100Time [h]

atte

nuat

ion

[%],

tem

pera

ture

[K]

attenuation temperature changing point

0 20 40 60 80 100Time [h]

atte

nuat

ion

[%],

tem

pera

ture

[K]



• Comparison in the relationship between temperature and “changing points”

Brewery F Brewery A

- Lower start temperature and later temperature increase : No temperature control at the “log phase (45-70h)”

1st CP IP

1st CP IP


0 20 40 60 80 100Time [h]

atte

nuat

ion

[%],

tem

pera

ture

[K]


1st CP IP


• Change in temperature pattern on Brewery F Start temperature : Conventional value +1 ºC Temperature increase time : 60h → 72h (Inflexion point : 70h)

Before After

- Temperature control at the “log phase”

0 20 40 60 80 100Time [h]

atte

nuat

ion

[%],

tem

pera

ture

[K]


1st CP IP


0

1

2

3

4

5

Sco

re o

f "S

ulph

ury"

in s

enso

ry te

st

Brewery F Average of 7 breweries

• Sensory test for monthly sample of Brand X


Pattern change


Result : Cases of process improvement with curve fitting

• We put this method into practical use to find out the appropriate time for temperature control to … Case (1) : Decrease sulphury flavour Case (2) : Increase ester aroma


15

17

19

21

23

25E

thyl

Ace

tate

[mg/

100m

l]

Brewery A Brewery B

Example２：Control of ester with temperature

• Monthly data of brand Y

- The amount of ester in brewery A had never reached to the target value.

Target value



• “Cooling in the latter” to prolong the stationary phase

- Appropriate cooling leads increase of esters. - Too early cooling could result in inadequate attenuation.

0 40 80 120 160 200 240 Time [h]

Temperature

Extract Yeast



- Cooling after the Inflexion point (=start of the stationary phase)

• “Cooling in the latter” to prolong the stationary phase

0 50 100 150 200

Time [h]

Atte

nuat

ion

[%]

2nd CP : 122h

-1 ℃ Cooling

IP : 75h



• Monthly data of brand Y

- The amount of ester in brewery A have reached to the target value.

Target value

Pattern change

15

17

19

21

23

25E

thyl

Ace

tate

[mg/

100m

l]

Brewery A Brewery B

Target value


Summery

•In this study, we examined curve-fitting method to analyze the attenuation data in beer fermentation.

•We could obtain the changing point with mathematical method, which would suggest the information about yeast growth phase.

•This method would help us to “when to do” the action to control fermentation, even in the industrial brewing.


Thank you for your kind attention!!

Taku Irie Production Technology Center

Asahi Breweries, Ltd. E-mail : [email protected]

Documents

Analysis of sugar attenuation with curve- fitting method