UNIT OPERATIONS
OF CHEMICAL ENGINEERING
WHAT IS UNIT OPERATIONS?
• It is a tool to handle problem of physical change.
• It is derived by a combination of science &
Engineering Principles.
• The Unit Operations can be applied to widely
divergent manufacturing procedures with no change
in concept, i.e these do not involve any chemical
reaction but only some of physical form is altered.
A LIST OF MAJOR UNIT OPERATIONS CARRIED OUT
Absorption
Adsorption
Crystallization
Distillation
Drying
Evaporation
Extraction
Centrifuging
Heat Exchanger
Scrubbing
Filtration
Mixing
Size reduction
ABSORPTION
• The process of absorption means that a substance captures &
transforms energy.
• The Absorbent distributes the material it captures throughout
whole & absorbent only distributes it through the surface.
• The process of gas or Liquid which penetrate into the body of
absorbent is commonly known as absorption.
TYPES OF ABSORPTION
1) Physical Absorption
• When water & Hydrocarbon oils are used as Absorbents, no significant
chemical reactions occur between the absorbent & the solute, & the process
is commonly referred to as Physical Absorption.
2) Chemical Absorption
• When aqueous sodium hydroxide is used as the absorbent to dissolve an acid
gas, absorption is accompanied by a rapid & irreversible neutralization
reaction in the liquid phase & the process is referred to as chemical
absorption or reactive absorption.
ADSORPTION
Adsorption is a Surface Phenomenon.
The process of taking up substances from solution on surface is
called Adsorption.
The greater the surface of adsorbing agent, the greater is the
adsorption.
Types of Adsorption:
1. Physical Adsorption
2. Chemical Adsorption
1. Physical Adsorption
• This type of adsorption is
caused by physical forces.
• Physisorption is a weak
phenomenon
• It is multilayered process
• This adsorption is not specific &
takes place all over the
adsorbent.
• Surface area, temperature,
pressure, nature of adsorbate
effects physisorption.
2. Chemical Adsorption
• It is due to strong chemical
forces of bonding type between
Adsorbate & Adsorbent.
• Adsorption of gas on a solid is
a spontaneous exothermic
reaction.
• Single layered phenomenon
• Highly Specific & takes place at
reaction centers.
EVAPORATION
• It refers to the process of Heating liquid to the boiling point to remove water
as vapour.
• The driving force for heat transfer is the difference in temperature between
the steam in the coils & the product in the pan. The steam is produced in
large boilers.
• The steam temperature is a function of the steam pressure. Water boils at
100°C at 1 atm., the product is also at its boiling point. The boiling point can
be elevated with an increase in solute concentration.
• Types of Evaporation:
1. Single effect Evaporation
2. Multiple effect Evaporation
CRYSTALLIZATION
• The principle of Crystallization is based on the limited solubility of a
compound in solvent at a certain temperature, pressure, etc.
• A change of these conditions to a state where the solubility is lower
will lead to the formation of crystalline solid.
• Crystallization is the process by which a solid forms where the
atoms or molecules are highly organized into a structure known as
a Crystal.
• The types of Crystallization are:
1. Evaporative Crystallization
2. Cooling Crystallization
3. Reactive Crystallization
DISTILLATION
• Distillation is a method of separating mixtures based on differences in volatility
(vapour pressure) of the components in a boiling liquid mixture.
• It is a Unit Operation, or a physical separation process, & not a chemical
reaction.
• It is used in pharmacy either to extract volatile active particles from vegetable
drugs or to separate volatile substances from less volatile impurities.
• Water is heated to boiling in an enclosed container. As the water evaporates,
inorganic chemicals, large non-volatile organic chemicals are left behind in the
boiling chamber.
TYPES OF DISTILLATION:
1) Simple Distillation
• The process of simple distillation is performed in various labs & this is the most basic &
simplest process of the distillation system.
• It involves the boiling of the flask. The solution is heated in the boiling flask till the time it
turns into the vapor.
• The solution is further cooled down in the condenser & goes to the receiver flask.
Advantages
• Simple setup
• Faster Distillation
• Less Energy Consumes
Disadvantages
• Impurities
• Azeotropic Mixture
• Large Boiling Point Difference
2) Fractional Distillation
• Fractional Distillation repeats the process several times within the
same system.
• Fractional distillation is ideal for a mixture whose components have
very close boiling points.
Advantages
• Easy to Implement
• Highly effective & Efficient
• Produce Much needed Fuel
Disadvantages
• Expensive
• Operational Hazards
• Environmental Pollution
3) Steam Distillation
• Steam Distillation is used to distil compounds at temperature lower
than the normal boiling point.
• Types of Steam Distillation:
1) External Steam Distillation
• Steam is generated outside the tank in a steam generator or
some boiler. The sample to be extracted is supported above the
steam inlet.
Advantages
• Steam intake can be
controlled according to
need of that procedure.
• Thermal decomposition
can be avoided
• Used for high boiling
oils.
Disadvantages
• Highly expensive
procedure
2) Internal Steam Distillation
• Substance to be separated & water is placed in a flask & thus
steam source is present inside the apparatus.
Advantages
• By changing amount of water in
distillation mixture, the water
content in steam can be adjusted.
Disadvantages
• Difficult to handle due to
complication of apparatus
• Prolonged contact with water
causes damage to material to be
distilled
• Presence of water in end
product.
• Time consuming.
4) Molecular Distillation
• Short path Distillation is Known as Molecular Distillation.
• It is considered as the safest means of separation for purifying thermally
unstable substances with other related compounds that have elevated boiling
point & low volatility, such as vitamins, clove oil, fish oil, ginger oil, etc.
Advantages
• Short residence time of the feed
liquid
• Low evaporation temperature.
• Non-toxic, harmless
• High efficiency
Disadvantages
• Highly Expensive
5) Azeotropic Distillation
• It is a process to break azeotrope where another volatile component, called
the entrainer, the solvent, or the mass separating agent (MSA), is added to
form a new lower-boiling Azeotrope that is heterogeneous.
Advantages
• Required less energy
• Equipments are easy to use
& Durable
• Less Risky
Disadvantages
• Azeotropic Mixtures cannot be
separated by Fractional
distillation either & typically
require other approaches.
DRYING
• Drying is defined as the removal of a liquid (moisture content)
from a material by the application of heat & accomplished by the
transfer of a liquid from a surface into an unsaturated vapour
phase.
• Drying is a mass transfer process consisting of the removal of
water or another solvent by evaporation from a solid, semi-solid
or liquid.
• Types of Drying:
1) Direct Drying
2) Indirect Drying
3) Radiation
EXTRACTION
• This is a process in which one or more components are separated
selectively from a liquid or solid mixture.
• Extractions are a way to separate a desired substance when it is
mixed with others.
• The mixtures is brought into contact with a solvent in which the
substance of interest is soluble, but the other substances present
are insoluble.
• The three most common types of extraction are:
1) Liquid/Liquid
2) Liquid/Solid
CENTRIFUGATION
• Works by using the principle of sedimentation under the influence
of Gravitational force, Substances separate according to their
density.
• A centrifuge is a device, generally driven by an electric motor, that
puts an object, in a rotational movement around a fixed axis.
• It is a device used to separate components of a mixture on the
basis of their size, density, the viscosity of the medium, & the rotor
speed.
• It is a technique of separating components where the centrifugal
force causes the denser molecules to move towards the periphery
while the less dense particles move to the center.
TYPES OF CENTRIFUGATION
1) Analytical Centrifugation
• Analytical Centrifugation is based on the principle that particles that are
denser than others settle down faster. Similarly, the large molecules move
more quickly in the centrifugal force than the smaller ones.
2) Differential Centrifugation
• Differential Centrifugation is based upon the differences in the sedimentation
rate of biological particles of different size & Density.
HEAT EXCHANGER
• A heat exchanger is a device which allows for fast & efficient transfer of heat
from one medium to another.
• The process works based upon the basic science of flow of heat, from hot to
cool medium.
• Types of Heat Exchanger:
1) Shell & Tube Heat Exchanger
• It consists of a number of tubes mounted inside a cylindrical shell. Two fluids
can exchange heat, one fluid flows over the outside of the tubes while the
second fluid flows through the tubes. The fluid can be single or two phase &
can flow in a parallel or cross/counter flow arrangement.
Advantages
• Less expensive
• Can be used in systems with higher
operating temperature & pressure.
• Pressure drop across a tube cooler
is less.
• Tube leaks are easily located &
plugged since pressure test is
comparatively easy.
• Tubular coolers in refrigeration
system can act as receiver also
• Tube coolers may be preferred for
lubricating oil cooling because the
pressure differential.
Disadvantages
• heat transfer efficiency is less
compared to plate type cooler
• Cleaning & Maintenance is
difficult since a tube cooler
requires enough clearance at
one end to remove the tube
nest.
• Capacity of tube cooler can’t
be increased
• Requires more space in
comparison to plate coolers
2) PLATE HEAT EXCHANGER
• The plate heat exchanger is the exception. Metal plates
are used to transfer heat between two fluids.
• The plate is a metal shell, with spaces inside each plate
that act as hallways for fluids to travel through.
• There is a greater surface area in contact with the fluids,
so it has better rates of heat transfer compared to all
other types.
Advantages
• Simple & Control in size
• Efficiency is more
• Can be easily cleaned
• No extra space is required for
dismantling
• Capacity can be increased by
introducing plates in pairs
• Leaking plates can be removed in pairs,
if necessary without replacement
• Maintenance is simple
• Turbulent flow help to reduce deposits
which would interfere with heat
transfer.
Disadvantages
• Initial cost is high since titanium
plates are expensive
• Finding leakage is difficult
• Since pressure test is not as easy
as tube coolers
• Bonding material between plates
limits operating temperature of
the cooler
• Pressure drop caused by plate
cooler is higher than tube cooler.
DOUBLE – PIPE HEAT EXCHANGER
• It is called a double-pipe exchanger because one
fluid flows inside a pipe & the other fluid between
that pipe & another pipe that surrounds the first.
• Flow in this exchanger can be co-current or
counter current.
Advantages
• They can handle both high
pressures & high temperature
well
• Their parts have been
standardized due to their
popularity, allowing for easy
part sourcing & repair
• They are one of the most
flexible designs, allowing for
easy addition/removal of parts.
Disadvantages
• Limited to lower heat duties
than other, larger designs
• Leaking can occur, especially
when paired with more units
• The tubes are easily fouled &
difficult to clean without
disassembling the whole heat
exchanger
• Less efficient method
SCRUBBING
• Scrubbers are devices to control air pollution & Used to remove some particulates & gases
from industrial exhaust streams.
• In the scrubber system, the exhaust gas is passed in the column from downside & scrubbing
solution is sprayed at top.
• The two main types of scrubbers are Wet scrubber & Dry scrubber.
1) Wet Scrubbers
• Wet scrubbers force the polluted fumes to pass through a wet limestone slurry which traps
sulfur particles.
• These can be used to control particulate matter less than 10 micrometers as well as inorganic
gases such as SO2, H2S, NH3, & various chlorides & Fluorides. Wet Scrubbers may also be
useful to control volatile organic compounds.
2) Dry Scrubbers
• Dry Scrubbers have an efficiency of more than 90% for removing SO2 under the right
condition, but they are limited to small to medium sized power plants of about 200 MW.
FILTRATION
• Since the filter medium is permeable only to the fluid, it retains the solid particles &
permits only the fluid to pass through which is collected as the filtrate.
• Two types of Filtration
1) Surface/Screen Filtration
• It is a screening action by which pores or holes of medium prevent the passage of
solids.
• Mechanism involved: Straining & Impingement
• For this, plates with holes are used.
• Efficiency is defined in terms of mean or maximum pore size.
2) Depth filtration
• In this slurry penetrates to a point where the diameter of solid particles is greater than
that of the tortuous void or channel.
• Mechanism: Entanglement
• The solid are retained with a gradient density structure by physical restriction or by
adsorption properties of medium.
AGITATION
• The Agitation is achieved by movement of the heterogeneous
mass, to the impeller. The is due to mechanical Agitators, to the
rotation of on impeller.
• Types of Agitators:
1)Paddle
2)Anchor
3)Radial
4)Propeller
5)Turbine
6)Helical
SIZE REDUCTION
• Size reduction is a mechanical process of breakdown of solids into smaller size
particles without altering the state of aggregation of solids.
• Size reduction causes particles breakage by subjecting the material to contact
forces or stresses.
• The applied forces cause deformation that generates internal stress in the
particles & when this stress reaches a certain level, particle breakage occurs.
• Types of size reduction Machinery
1) Impact – hitting material causing fractures.
2) Shear – tearing or Ripping
3) Compression – breaking material by squeezing
4) Attrition – material pieces colliding with each other causing reduction

Unit Operations of chemical Engineering.

  • 1.
  • 2.
    WHAT IS UNITOPERATIONS? • It is a tool to handle problem of physical change. • It is derived by a combination of science & Engineering Principles. • The Unit Operations can be applied to widely divergent manufacturing procedures with no change in concept, i.e these do not involve any chemical reaction but only some of physical form is altered.
  • 3.
    A LIST OFMAJOR UNIT OPERATIONS CARRIED OUT Absorption Adsorption Crystallization Distillation Drying Evaporation Extraction Centrifuging Heat Exchanger Scrubbing Filtration Mixing Size reduction
  • 4.
    ABSORPTION • The processof absorption means that a substance captures & transforms energy. • The Absorbent distributes the material it captures throughout whole & absorbent only distributes it through the surface. • The process of gas or Liquid which penetrate into the body of absorbent is commonly known as absorption.
  • 5.
    TYPES OF ABSORPTION 1)Physical Absorption • When water & Hydrocarbon oils are used as Absorbents, no significant chemical reactions occur between the absorbent & the solute, & the process is commonly referred to as Physical Absorption. 2) Chemical Absorption • When aqueous sodium hydroxide is used as the absorbent to dissolve an acid gas, absorption is accompanied by a rapid & irreversible neutralization reaction in the liquid phase & the process is referred to as chemical absorption or reactive absorption.
  • 6.
    ADSORPTION Adsorption is aSurface Phenomenon. The process of taking up substances from solution on surface is called Adsorption. The greater the surface of adsorbing agent, the greater is the adsorption. Types of Adsorption: 1. Physical Adsorption 2. Chemical Adsorption
  • 7.
    1. Physical Adsorption •This type of adsorption is caused by physical forces. • Physisorption is a weak phenomenon • It is multilayered process • This adsorption is not specific & takes place all over the adsorbent. • Surface area, temperature, pressure, nature of adsorbate effects physisorption. 2. Chemical Adsorption • It is due to strong chemical forces of bonding type between Adsorbate & Adsorbent. • Adsorption of gas on a solid is a spontaneous exothermic reaction. • Single layered phenomenon • Highly Specific & takes place at reaction centers.
  • 8.
    EVAPORATION • It refersto the process of Heating liquid to the boiling point to remove water as vapour. • The driving force for heat transfer is the difference in temperature between the steam in the coils & the product in the pan. The steam is produced in large boilers. • The steam temperature is a function of the steam pressure. Water boils at 100°C at 1 atm., the product is also at its boiling point. The boiling point can be elevated with an increase in solute concentration. • Types of Evaporation: 1. Single effect Evaporation 2. Multiple effect Evaporation
  • 9.
    CRYSTALLIZATION • The principleof Crystallization is based on the limited solubility of a compound in solvent at a certain temperature, pressure, etc. • A change of these conditions to a state where the solubility is lower will lead to the formation of crystalline solid. • Crystallization is the process by which a solid forms where the atoms or molecules are highly organized into a structure known as a Crystal. • The types of Crystallization are: 1. Evaporative Crystallization 2. Cooling Crystallization 3. Reactive Crystallization
  • 10.
    DISTILLATION • Distillation isa method of separating mixtures based on differences in volatility (vapour pressure) of the components in a boiling liquid mixture. • It is a Unit Operation, or a physical separation process, & not a chemical reaction. • It is used in pharmacy either to extract volatile active particles from vegetable drugs or to separate volatile substances from less volatile impurities. • Water is heated to boiling in an enclosed container. As the water evaporates, inorganic chemicals, large non-volatile organic chemicals are left behind in the boiling chamber.
  • 11.
    TYPES OF DISTILLATION: 1)Simple Distillation • The process of simple distillation is performed in various labs & this is the most basic & simplest process of the distillation system. • It involves the boiling of the flask. The solution is heated in the boiling flask till the time it turns into the vapor. • The solution is further cooled down in the condenser & goes to the receiver flask. Advantages • Simple setup • Faster Distillation • Less Energy Consumes Disadvantages • Impurities • Azeotropic Mixture • Large Boiling Point Difference
  • 12.
    2) Fractional Distillation •Fractional Distillation repeats the process several times within the same system. • Fractional distillation is ideal for a mixture whose components have very close boiling points. Advantages • Easy to Implement • Highly effective & Efficient • Produce Much needed Fuel Disadvantages • Expensive • Operational Hazards • Environmental Pollution
  • 13.
    3) Steam Distillation •Steam Distillation is used to distil compounds at temperature lower than the normal boiling point. • Types of Steam Distillation: 1) External Steam Distillation • Steam is generated outside the tank in a steam generator or some boiler. The sample to be extracted is supported above the steam inlet.
  • 14.
    Advantages • Steam intakecan be controlled according to need of that procedure. • Thermal decomposition can be avoided • Used for high boiling oils. Disadvantages • Highly expensive procedure
  • 15.
    2) Internal SteamDistillation • Substance to be separated & water is placed in a flask & thus steam source is present inside the apparatus. Advantages • By changing amount of water in distillation mixture, the water content in steam can be adjusted. Disadvantages • Difficult to handle due to complication of apparatus • Prolonged contact with water causes damage to material to be distilled • Presence of water in end product. • Time consuming.
  • 16.
    4) Molecular Distillation •Short path Distillation is Known as Molecular Distillation. • It is considered as the safest means of separation for purifying thermally unstable substances with other related compounds that have elevated boiling point & low volatility, such as vitamins, clove oil, fish oil, ginger oil, etc. Advantages • Short residence time of the feed liquid • Low evaporation temperature. • Non-toxic, harmless • High efficiency Disadvantages • Highly Expensive
  • 17.
    5) Azeotropic Distillation •It is a process to break azeotrope where another volatile component, called the entrainer, the solvent, or the mass separating agent (MSA), is added to form a new lower-boiling Azeotrope that is heterogeneous. Advantages • Required less energy • Equipments are easy to use & Durable • Less Risky Disadvantages • Azeotropic Mixtures cannot be separated by Fractional distillation either & typically require other approaches.
  • 18.
    DRYING • Drying isdefined as the removal of a liquid (moisture content) from a material by the application of heat & accomplished by the transfer of a liquid from a surface into an unsaturated vapour phase. • Drying is a mass transfer process consisting of the removal of water or another solvent by evaporation from a solid, semi-solid or liquid. • Types of Drying: 1) Direct Drying 2) Indirect Drying 3) Radiation
  • 19.
    EXTRACTION • This isa process in which one or more components are separated selectively from a liquid or solid mixture. • Extractions are a way to separate a desired substance when it is mixed with others. • The mixtures is brought into contact with a solvent in which the substance of interest is soluble, but the other substances present are insoluble. • The three most common types of extraction are: 1) Liquid/Liquid 2) Liquid/Solid
  • 20.
    CENTRIFUGATION • Works byusing the principle of sedimentation under the influence of Gravitational force, Substances separate according to their density. • A centrifuge is a device, generally driven by an electric motor, that puts an object, in a rotational movement around a fixed axis. • It is a device used to separate components of a mixture on the basis of their size, density, the viscosity of the medium, & the rotor speed. • It is a technique of separating components where the centrifugal force causes the denser molecules to move towards the periphery while the less dense particles move to the center.
  • 21.
    TYPES OF CENTRIFUGATION 1)Analytical Centrifugation • Analytical Centrifugation is based on the principle that particles that are denser than others settle down faster. Similarly, the large molecules move more quickly in the centrifugal force than the smaller ones. 2) Differential Centrifugation • Differential Centrifugation is based upon the differences in the sedimentation rate of biological particles of different size & Density.
  • 22.
    HEAT EXCHANGER • Aheat exchanger is a device which allows for fast & efficient transfer of heat from one medium to another. • The process works based upon the basic science of flow of heat, from hot to cool medium. • Types of Heat Exchanger: 1) Shell & Tube Heat Exchanger • It consists of a number of tubes mounted inside a cylindrical shell. Two fluids can exchange heat, one fluid flows over the outside of the tubes while the second fluid flows through the tubes. The fluid can be single or two phase & can flow in a parallel or cross/counter flow arrangement.
  • 23.
    Advantages • Less expensive •Can be used in systems with higher operating temperature & pressure. • Pressure drop across a tube cooler is less. • Tube leaks are easily located & plugged since pressure test is comparatively easy. • Tubular coolers in refrigeration system can act as receiver also • Tube coolers may be preferred for lubricating oil cooling because the pressure differential. Disadvantages • heat transfer efficiency is less compared to plate type cooler • Cleaning & Maintenance is difficult since a tube cooler requires enough clearance at one end to remove the tube nest. • Capacity of tube cooler can’t be increased • Requires more space in comparison to plate coolers
  • 24.
    2) PLATE HEATEXCHANGER • The plate heat exchanger is the exception. Metal plates are used to transfer heat between two fluids. • The plate is a metal shell, with spaces inside each plate that act as hallways for fluids to travel through. • There is a greater surface area in contact with the fluids, so it has better rates of heat transfer compared to all other types.
  • 25.
    Advantages • Simple &Control in size • Efficiency is more • Can be easily cleaned • No extra space is required for dismantling • Capacity can be increased by introducing plates in pairs • Leaking plates can be removed in pairs, if necessary without replacement • Maintenance is simple • Turbulent flow help to reduce deposits which would interfere with heat transfer. Disadvantages • Initial cost is high since titanium plates are expensive • Finding leakage is difficult • Since pressure test is not as easy as tube coolers • Bonding material between plates limits operating temperature of the cooler • Pressure drop caused by plate cooler is higher than tube cooler.
  • 26.
    DOUBLE – PIPEHEAT EXCHANGER • It is called a double-pipe exchanger because one fluid flows inside a pipe & the other fluid between that pipe & another pipe that surrounds the first. • Flow in this exchanger can be co-current or counter current.
  • 27.
    Advantages • They canhandle both high pressures & high temperature well • Their parts have been standardized due to their popularity, allowing for easy part sourcing & repair • They are one of the most flexible designs, allowing for easy addition/removal of parts. Disadvantages • Limited to lower heat duties than other, larger designs • Leaking can occur, especially when paired with more units • The tubes are easily fouled & difficult to clean without disassembling the whole heat exchanger • Less efficient method
  • 28.
    SCRUBBING • Scrubbers aredevices to control air pollution & Used to remove some particulates & gases from industrial exhaust streams. • In the scrubber system, the exhaust gas is passed in the column from downside & scrubbing solution is sprayed at top. • The two main types of scrubbers are Wet scrubber & Dry scrubber. 1) Wet Scrubbers • Wet scrubbers force the polluted fumes to pass through a wet limestone slurry which traps sulfur particles. • These can be used to control particulate matter less than 10 micrometers as well as inorganic gases such as SO2, H2S, NH3, & various chlorides & Fluorides. Wet Scrubbers may also be useful to control volatile organic compounds. 2) Dry Scrubbers • Dry Scrubbers have an efficiency of more than 90% for removing SO2 under the right condition, but they are limited to small to medium sized power plants of about 200 MW.
  • 29.
    FILTRATION • Since thefilter medium is permeable only to the fluid, it retains the solid particles & permits only the fluid to pass through which is collected as the filtrate. • Two types of Filtration 1) Surface/Screen Filtration • It is a screening action by which pores or holes of medium prevent the passage of solids. • Mechanism involved: Straining & Impingement • For this, plates with holes are used. • Efficiency is defined in terms of mean or maximum pore size. 2) Depth filtration • In this slurry penetrates to a point where the diameter of solid particles is greater than that of the tortuous void or channel. • Mechanism: Entanglement • The solid are retained with a gradient density structure by physical restriction or by adsorption properties of medium.
  • 30.
    AGITATION • The Agitationis achieved by movement of the heterogeneous mass, to the impeller. The is due to mechanical Agitators, to the rotation of on impeller. • Types of Agitators: 1)Paddle 2)Anchor 3)Radial 4)Propeller 5)Turbine 6)Helical
  • 31.
    SIZE REDUCTION • Sizereduction is a mechanical process of breakdown of solids into smaller size particles without altering the state of aggregation of solids. • Size reduction causes particles breakage by subjecting the material to contact forces or stresses. • The applied forces cause deformation that generates internal stress in the particles & when this stress reaches a certain level, particle breakage occurs. • Types of size reduction Machinery 1) Impact – hitting material causing fractures. 2) Shear – tearing or Ripping 3) Compression – breaking material by squeezing 4) Attrition – material pieces colliding with each other causing reduction