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The goal of this reference book, available for the first time in English, is to provide an overview of the technological calculations and benchmarks relevant to those in the brewing and malting industries. The authors supplement this overview with correlations and statistically reliable relationships they have researched during their carriers. For trainees, students, and practitioners of brewing, malting, and beverage sciences, this book will help to optimize process management. Furthermore helpful technological calculation tables and graphs are included to create an easy to use reference book.

In addition to the computational principles, numerous sample calculations, in the form of real world examples, are explained and carried out to provide a deeper understanding of the discussed topics. From these principles and examples, the reader can easily implement company specific solutions. For smaller breweries, which may lack the data for a large analytical study, simplified technological approximations are also suggested. Since the book has its origin in Germany, metric system units are used in all calculations.

From the content: Basic and geometric calculations / Grain storage, care, transportation / Malt production and milling / Brewing water and cleaning agents / Wort production / Fermentation and maturation of beer / Clarification and stabilization of Beer / Thermal preservation of beer / Energy content of beer and alcohol breakdown in the human body / Sample calculations for preparation of alcohol-free soft drinks / Product pipelines in the brewery / Utilities: Pumps / compressors / heat exchangers / Key indicators for plant planning / Units

Translated by Christopher Bergtholdt

## Applied Mathematics for Malting and Brewing Technologists

## Abbreviations and Symbols

## Overview of Calculation examples

## Preface

## Some hints for rule of three, percentage, and interest calculations and for simple statistics

### Notes on basic math operations

Rule of three calculations by direct proportion to base and partial amounts

Rule of three calculations by Inverse proportion to base and partial amounts

Percentage calculations

Interest calculations

Mixing calculations and their expanded applications

#### Requirements and notes for the application of mixing calculations

Calculating with a mixing cross

Mixing calculations with a general equation

### Application of statistical methods for the evaluation of test results (a short overview for beginners)

#### Preliminary observations

Error types

Population

Statistical quality assurance

Sampling

Characterizing the numeric values of a measurement

Statistical testing methods, statistical reliability P and
probability of error α

Test distributions

Degrees of freedom f

Confidence interval Δ x̄ of an average value

Outliers

Outlier tests

Empirical frequency distributions

Comparison between two means with the t-test

Two-dimensional (linear, simple) regression and correlation analysis

Multiple linear correlation and regression analysis

## Container geometry - calculations of areas, volumes and filling capacity in malteries and breweries

### The calculation of areas for standard shapes

#### The rectangle and the square

The parallelogram

The trapezoid

The triangle

The circle

The annulus

The ellipse

### Example calculations using surface area equations

Calculation of internal volume V from the main vessels that are of
importance for malteries and breweries

#### The cuboid

The cone and truncated cone

The pyramid and truncated pyramid

The sphere and spherical dome

The cylinder

### Some example calculations for the maltery and brewery employing volume equations

## Storage of grains, grain care and grain transport

### The calculation of potential storage losses in freshly harvested grain

#### Technological significance and standard values

Balance equations of the material conversion of stored barley

Calculation of the loss of substance, oxygen demand, CO_{2}- and
water formation during storage of barley

Calculating the warming experienced by stored barley

### The preliminary storage of freshly harvested grains without preservatives
and without aeration

Aeration of grain during the pre-storage phase with atmospheric air
and with cooled air

The grain drying

The aeration and cooling of grain

#### Required amount of air

Pressure losses in the grain bill

### Internal transportation of grains

#### Belt conveyor

Elevator

Screw conveyors

Trough chain conveyor

Tubular drag chain conveyors

Pneumatic conveying

### Converting batches of grains to a basic moisture content

Cleaning and sorting a barley charge

#### Technological aim of the maltery:

### Storage space required for grains

## Malt production

### Calculation of steeping degree

Calculation of the necessary steeping space

Water requirements during steeping

Temperature regulation, CO_{2}-removal and water consumption
during steeping

Germination box capacity

Germination air consumption, cooling, humidity of the germination air and energy requirements, design of kiln

ventilation fans and electric power consumption, pressure drop calculations in pipe channels of
gases

and vapors

h,x-diagram in the maltery

#### General notes

Thermodynamic laws

The h,x-diagram for moist air

Important changes in state

### Assessment of malting processes and malt quality

#### Overall leaf sprout length

Malting yield, malting losses and malting factor

### Sprouting rootlets malt germs

## Milling of malt (grist)

### Reference values for malt grist

Assessment of lauter tun grist

Wetting of grains before milling or grinding

Grist volume

## Calculations for brewing water and alkaline cleaners

### Reference values and technological definitions of brewing water

Useful conversions for water chemistry

Notes on the analysis of water salts and their calculation

Calculation of the residual alkalinity (RA) of brewing water

Decarbonization of brewing water with lime water

#### Chemical reactions

Determination of the concentration of the lime water

Concentration determination of dissolved CO_{2} content of raw water

Calculation of the required amount of lime water for the reduction
of the carbonate hardness in raw water

Required total quantity of lime water

### Estimation of the mash pH value as a function of the malt quality and
the residual alkalinity of brewing water

Reduction of the residual alkalinity of mashing water through the
addition of Ca ions

Determination of the cleaning effect of alkaline cleaning solutions

## Wort production

### Striking and brewhouse yield

#### Required amount of main strike as a function of the desired first
wort concentration

Calculation of total mash volume and required mash container volume

Calculation of the required water quantity for the sparging

Volume of first wort and kettle-full wort per brew

Calculating the brewhouse yield

Calculation of the projected amount of hot knockout wort

Required total evaporation, in relation to kettle full wort

Estimation of spent grain per brew

Required water quantity for the production of wort

### Adjusting the pH value in mash and wort

#### Technical definitions

Guidelines for acidification with lactic acid

### Calculation of the mash temperature steps (decoction)

Mash tun heating

#### Heat transfer

Calculation of heat quantities and heating surfaces

The design of heat transfer surfaces on brewing vessels

Temperature increase by mixed condensation

### Lautering the wort

#### Technological summary

Some guidelines for the lautering process

Demonstrating the influence of the grain height and the influence of
the material characteristics of the lauter wort on the lautering speed

Influence of lautering technology when discharging the grains on the porosity of the grain cake in the lauter tun

Calculation of the required mashing capacity of a mash filter

Required size of spent grain silos

Extract content of last runnings

### Boiling of wort

#### Technological goals and important guidelines for wort boiling

The water evaporation during seasoning and the necessary energy expenditure

### Bitterness dosage and utilization

#### Orientation values for bitterness utilization (Y_{Bit}) in wort and for bitterness losses from the pitching yeast to finished beer resulting
from the

use of different technological procedures

Calculation of the required amount of hops and bitterness

Simplified calculation of the yield of bitterness in the brewery and correction of the α-acid consumption per hectoliter of kettle full
wort (cold)

Simplified calculation of the bitterness utilization Y_{Bit} in relation to the finished beer

### Calculations to change the grist composition

#### Calculation of the desired malt color for a malt mix

A simple method for the conversion of extracts by malt surrogates for extract balancing by means of brewhouse yield

### Extract yield and yield balance

#### Standard values for the evaluation of extract yields

Calculation of the classic brewhouse yield Y_{BH}

Assessment of extract extraction by the method ”Overall Brewhouse
Yield“ (Y_{OBY})

Necessary clarification of the addition and recovery of extract by
the use of last runnings and trub

Example of an extract balance in connection with the corresponding
spent grain analysis

### The cooling of the knockout wort to pitching temperature and variants to the utilization of the liquid heat exchange

#### Comparison of wort cooling variants by means of model calculations

Results of a model calculation and conclusions

## Fermentation and maturation of beer

### Calculations for brewery yeast

#### Physical reference values for yeast cells and their influence on
the effective metabolic area of the yeast

The density of yeast cells and their sedimentation behavior

The yeast content of different yeast products and their influences
on yeast growth

The size of yeast cells and their influence on the clarification behavior

The multiplication kinetics of yeast and their influence on the
interrelation of yeast propagation plants

Calculation of the required oxygen and air input for yeast multiplication
in beer wort

### Fermentation, degree of fermentation, original gravity, speed of fermentation

#### Metabolic cycles in the process of fermentation and original
gravity of beer

Fermentation and degree of attenuation

The resulting amount of water from 1000 g of wort

Volume conversion of wort and beer

Assessment of a young beer during hosing

Alcohol and extract calculations according to *Tabarié*

### The fermentable residual extract at the time of bunging, the maximum possible CO_{2} formation, and the calculation of the

required amount
of “speise” (feed) for bottle fermentation

The speed of fermentation

#### Average decrease of the apparent extract in the initial and main fermentation phase every 24 h

The average fermentation per unit of volume

Technological influence on the average fermentation

Specific extract metabolism per yeast cell

Fermentation rate according to *Schröderheim*

### Calculation of the bunging pressure

## Clarification and stabilization of beer

### Objectives and process steps

Calculating the diatomaceous earth dosage

#### Pre-coating

Filtration time and running dosages

Differential pressure increase and filtration time

### Filter aid preparation

Crossflow membrane filtration (CMF)

Preparation using the protein stabilizer silica gel

## Thermal preservation of beer (pasteurization)

### Aims, definitions and recommended values

Flash pasteurization

Bottle pasteurization in a tunnel pasteurizer

The D-value and z-value as determined guideline values for killing
special microorganisms

## Energy content of beer and alcohol breakdown in the human body

### Energy equivalence of beer components

Beer consumption and blood alcohol content

## Filling

### Gas diffusion

Storage capacity of a bottle buffering belt

Caustic carryover in a bottle cleaning machine (BCM)

Vapor suction in a bottle cleaning machine (BCM)

Forklifts

Acceptance of filling installations, guarantees

#### General information

Results of acceptance and determination of consumption values

International acceptance and determination of consumption values

Important terms for the assessment of filling systems

Time concepts

### Compliance with the nominal filling quantity

#### Terms

Filling quantity requirements for marking by mass or volume

Calculation notes

Consequences of underfilling or overfilling

### The space requirement for the storage of empty and full bottles

The space and room requirement for filling systems

## Sample calculations for preparation of alcohol-free soft drinks

### Overview and basic requirements

Batch calculation for a lemon lemonade

The sugar-acid ratio

Reduced calorific value of alcohol-free soft drinks

The carbonization of alcohol-free soft drinks

#### CO_{2} solubility, guideline values and definitions

Calculations to adjust the CO_{2} concentration in water and sodas

## Product pipelines in the brewery

### Important aspects for the design of pipelines in the beverage industry

#### The flow rate

The pressure loss when a pipe or fitting is passed through

Pressure loss estimation by means of nomogram for liquids

The *Reynolds* number

The boundary layer thickness

### The flow rate during product conveyance

Instructions for the design of pipelines

#### General information

Thermally induced changes in length

Bleeding of pipelines, oxygen removal

## Pumps

### Geodetic height

Efficiency of the drive motors

Cavitation

Power requirement of a centrifugal pump

Note on pump selection

#### Characteristics and ways of influencing them

Starting conditions:

## Compressors

### General information

Power supply for compressors

Notes on the use of compressors

#### Possibilities for improving efficiency

Notes on compressors in the beverage industry

General information on compressors

## Heat exchanger

### Heat transfer

Heat transfer coefficients

General information on the calculation for heat exchanger

Thermal dimensioning

Mean logarithmic temperature difference

## Indicators for plant planning

### Raw material

Balance equations respiration and fermentation

Specific heat capacities

Specific brewery consumption values

Specific characteristics for a maltery

#### Consumption values

Specific load/capacity in the maltery

Malting losses

Energy consumption values

Electricity

Water demand/waste water

### Specific consumption values bottle cleaning

Specific volumes for brewing vessels, characteristic values for
Brewhouses

CCV for fermentation, maturation and lagering

Filter systems for beer

Extract and volume contraction

Selected values for steam and water

Characteristics of selected packaging materials

## Physical-technical units in the brewing and malting industry

## Index

## Bibliography and Sources

Format: 6.5" x 9.5" softcover

Pages: 365

Publication Weight: 3 lbs