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Applied Mathematics for Malting and Brewing Technologists
Applied Mathematics for Malting and Brewing Technologists
This book will help to optimize process management for trainees, students, and practitioners of brewing, malting, and beverage sciences.

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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


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
Statistical quality assurance
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
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, CO2- 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
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, CO2-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 CO2 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 (YBit) 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 YBit 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 YBH
Assessment of extract extraction by the method ”Overall Brewhouse Yield“ (YOBY)
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 CO2 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

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


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)
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

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

CO2 solubility, guideline values and definitions
Calculations to adjust the CO2 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


Geodetic height
Efficiency of the drive motors
Power requirement of a centrifugal pump
Note on pump selection

Characteristics and ways of influencing them
Starting conditions:


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
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


Bibliography and Sources

Publish Date: 2017
Format: 6.5" x 9.5" softcover
Pages: 365
Publication Weight: 3 lbs

By Gerolf Annemüller and Hans-J. Manger

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