Heat Exchanger Design

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Heat Exchanger Design

• Anand V P Gurumoorthy
• Associate Professor
• Chemical Engineering Division
• School of Mechanical Building Sciences
• VIT University
• Vellore, India

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Heat Exchanger Classification

• Recuperative
• Cold and hot fluid flow through the unit without
  mixing with each other. The transfer of heat
  occurs through the metal wall.
• Regenerative
• Same heating surface is alternately exposed to
  hot and cold fluid. Heat from hot fluid is stored
  by packings or solids this heat is passed over
  to the cold fluid.
• Direct contact
• Hot and cold fluids are in direct contact and
  mixing occurs among them mass transfer and heat
  transfer occur simultaneously.

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Heat Exchanger Standards and Codes

• British Standard BS-3274
• TEMA standards are universally used.
• TEMA standards cover following classes of
  exchangers
• Class R designates severe requirements of
  petroleum and other related processing
  applications
• Class C moderate requirements of commercial and
  general process applications
• Class B specifies design and fabrication for
  chemical process service.

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Shell and Tube Heat Exchanger

• Most commonly used type of heat transfer
  equipment in the chemical and allied industries.
• Advantages
• The configuration gives a large surface area in a
  small volume.
• Good mechanical layout a good shape for pressure
  operation.
• Uses well-established fabrication techniques.
• Can be constructed from a wide range of
  materials.
• Easily cleaned.
• Well established design procedures.

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Types of Shell and Tube Heat Exchangers

• Fixed tube design
• Simplest and cheapest type.
• Tube bundle cannot be removed for cleaning.
• No provision for differential expansion of shell
  and tubes.
• Use of this type limited to temperature
  difference upto 800C.
• Floating head design
• More versatile than fixed head exchangers.
• Suitable for higher temperature differentials.
• Bundles can be removed and cleaned (fouling
  liquids)

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Design of Shell and Tube Heat Exchangers

• Kern method
• Does not take into account bypass and leakage
  streams.
• Simple to apply and accurate enough for
  preliminary design calculations.
• Restricted to a fixed baffle cut (25).
• Bell-Delaware method
• Most widely used.
• Takes into account
• Leakage through the gaps between tubes and
  baffles and the baffles and shell.
• Bypassing of flow around the gap between tube
  bundle and shell.
• Stream Analysis method (by Tinker)
• More rigorous and generic.
• Best suited for computer calculations basis for
  most commercial computer codes.

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Construction Details Tube Dimensions

• Tube diameters in the range 5/8 inch (16 mm) to 2
  inch (50 mm).
• Smaller diameters (5/8 to 1 inch) preferred since
  this gives compact and cheap heat exchangers.
• Larger tubes for heavily fouling fluids.
• Steel tubes BS 3606 Other tubes BS 3274.
• Preferred tube lengths are 6 ft, 8 ft, 12 ft, 16
  ft, 20 ft and 24 ft optimum tube length to shell
  diameter ratio 5 10.
• ¾ in (19 mm) is a good starting trial tube
  diameter.

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Construction Details Tube Arrangements

• Tubes usually arranged in equilateral triangular,
  square or rotated square patterns.
• Tube pitch, Pt, is 1.25 times OD.

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Construction Details - Shells

• Shell should be a close fit to the tube bundle to
  reduce bypassing.
• Shell-bundle clearance will depend on type of
  heat exchanger.

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Construction Details - Shell-Bundle Clearance
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Construction Details Tube Count

• Bundle diameter depends not only on number of
  tubes but also number of tube passes.
• Nt is the number of tubes
• Db is the bundle diameter (mm)
• D0 is tube outside diameter (mm)
• n1 and K1 are constants

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Construction Details - Baffles

• Baffles are used
• To direct the fluid stream across the tubes
• To increase the fluid velocity
• To improve the rate of transfer
• Most commonly used baffle is the single segmental
  baffle.
• Optimal baffle cut 20-25

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Basic Design Procedure

• General equation for heat transfer is
• where Q is the rate of heat transfer (duty),
• U is the overall heat transfer coefficient,
• A is the area for heat transfer
• ?Tm is the mean temperature difference
• We are not doing a mechanical design, only a
  thermal design.

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Overall Heat Transfer Coefficient

• Overall coefficient given by
• h0 (hi) is outside (inside) film coefficient
• hod (hid) is outside (inside) dirt coefficient
• kw is the tube wall conductivity
• do (di) is outside (inside) tube diameters

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Individual Film Coefficients

• Magnitude of individual coefficients will depend
  on
• Nature of transfer processes (conduction,
  convection, radiation, etc.)
• Physical properties of fluids
• Fluid flow rates
• Physical layout of heat transfer surface
• Physical layout cannot be determined until area
  is known hence design is a trial-and-error
  procedure.

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Typical Overall Coefficients
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Typical Overall Coefficients
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Fouling Factors (Dirt Coeffs)

• Difficult to predict and usually based on past
  experience

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Mean Temperature Difference (Temperature Driving
Force)

• To determine A, ?Tm must be estimated
• True counter-current flow logarithmic
  temperature difference (LMTD)

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LMTD

• LMTD is given by
• where T1 is the hot fluid temperature, inlet
• T2 is the hot fluid temperature, outlet
• t1 is the cold fluid temperature, inlet
• t2 is the cold fluid temperature, outlet

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Counter-current Flow Temperature Proflies
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12 Heat Exchanger Temperature Profiles
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True Temperature Difference

• Obtained from LMTD using a correction factor
• ?Tm is the true temperature difference
• Ft is the correction factor
• Ft is related to two dimensionless ratios

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Temp Correction Factor Ft

• Temperature correction factor, one shell pass,
  two or more even tube passes

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Fluid Allocation Shell or Tubes?

• Corrosion
• Fouling
• Fluid temperatures
• Operating pressures
• Pressure drop
• Viscosity
• Stream flow rates

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Shell and Tube Fluid Velocities

• High velocities give high heat-transfer
  coefficients but also high pressure drop.
• Velocity must be high enough to prevent settling
  of solids, but not so high as to cause erosion.
• High velocities will reduce fouling
• For liquids, the velocities should be as follows
• Tube side Process liquid 1-2m/s
• Maximum 4m/s if required to reduce fouling
• Water 1.5 2.5 m/s
• Shell side 0.3 1 m/s

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Pressure Drop

• As the process fluids move through the heat
  exchanger there is associated pressure drop.
• For liquids viscosity lt 1mNs/m2 35kN/m2
• Viscosity 1 10 mNs/m2 50-70kN/m2

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Tube-side Heat Transfer Coefficient

• For turbulent flow inside conduits of uniform
  cross-section, Sieder-Tate equation is
  applicable
• C0.021 for gases
• 0.023 for low viscosity liquids
• 0.027 for viscous liquids
• µ fluid viscosity at bulk fluid temperature
• µwfluid viscosity at the wall

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Tube-side Heat Transfer Coefficient

• Butterworth equation
• For laminar flow (Relt2000)
• If Nu given by above equation is less than 3.5,
  it should be taken as 3.5

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Heat Transfer Factor, jh

• j factor similar to friction factor used for
  pressure drop
• This equation is valid for both laminar and
  turbulent flows.

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Tube Side Heat Transfer Factor
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Heat Transfer Coefficients for Water

• Many equations for hi have developed specifically
  for water. One such equation is
• where hi is the inside coefficient (W/m2 0C)
• t is the water temperature (0C)
• ut is water velocity (m/s)
• dt is tube inside diameter (mm)

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Tube-side Pressure Drop

• where ?P is tube-side pressure drop (N/m2)
• Np is number of tube-side passes
• ut is tube-side velocity (m/s)
• L is the length of one tube
• m is 0.25 for laminar and 0.14 for turbulent
• jf is dimensionless friction factor for heat
  exchanger tubes

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Tube Side Friction Factor
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Shell-side Heat Transfer and Pressure Drop

• Kerns method
• Bells method

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Procedure for Kerns Method

• Calculate area for cross-flow As for the
  hypothetical row of tubes in the shell equator.
• pt is the tube pitch
• d0 is the tube outside diameter
• Ds is the shell inside diameter
• lB is the baffle spacing, m.
• Calculate shell-side mass velocity Gs and linear
  velocity, us.
• where Ws is the fluid mass flow rate in the
  shell in kg/s

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Procedure for Kerns Method

• Calculate the shell side equivalent diameter
  (hydraulic diameter).
• For a square pitch arrangement
• For a triangular pitch arrangement

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Shell-side Reynolds Number

• The shell-side Reynolds number is given by
• The coefficient hs is given by
• where jh is given by the following chart

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Shell Side Heat Transfer Factor
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Shell-side Pressure Drop

• The shell-side pressure drop is given by
• where jf is the friction factor given by
  following chart.

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Shell Side Friction Factor
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(Figure 8 in notes)
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(Figure 4 in notes)
(Figure 2)
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(Figure 9 in notes)
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(Table 3 in notes)
(Figure 10 in notes)
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(Figure 12 in notes)
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Bells Method

• In Bells method, the heat transfer coefficient
  and pressure drop are estimated from correlations
  for flow over ideal tube banks.
• The effects of leakage, by-passing, and flow in
  the window zone are allowed for by applying
  correction factors.

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Bells Method Shell-side Heat Transfer
Coefficient

• where hoc is heat transfer coeff for cross flow
  over ideal tube banks
• Fn is correction factor to allow for no. of
  vertical tube rows
• Fw is window effect correction factor
• Fb is bypass stream correction factor
• FL is leakage correction factor

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Bells Method Ideal Cross Flow Coefficient

• The Re for cross-flow through the tube bank is
  given by
• Gs is the mass flow rate per unit area
• d0 is tube OD
• Heat transfer coefficient is given by

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Bells Method Tube Row Correction Factor

• For Regt2100, Fn is obtained as a function of Ncv
  (no. of tubes between baffle tips) from the chart
  below
• For Re 100ltRelt2100, Fn1.0
• For Relt100,

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Bells Method Window Correction Factor

• Fw, the window correction factor is obtained from
  the following chart
• where Rw is the ratio of bundle cross-sectional
  area in the window zone to the tube bundle
  cross-sectional area (obtained from simple
  formulae).

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Bells Method Bypass Correction Factor

• Clearance area between the bundle and the shell
• For the case of no sealing strips, Fb as a
  function of Ab/As can be obtained from the
  following chart

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Bells Method Bypass Correction Factor

• For sealing strips, for NsltNcv/2 (Ns is the
  number of baffle strips)
• where a1.5 for Relt100 and a1.35 for Regt100.

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Bells Method Leakage Correction Factor

• Tube-baffle clearance area Atb is given by
• Shell-baffle clearance area Asb is given by
• where Cs is baffle to shell clearance and ?b is
  the angle subtended by baffle chord
• ALAtbAsb
• where ßL is a factor obtained from following
  chart

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Coefficient for FL, Heat Transfer
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Shell-side Pressure Drop

• Involves three components
• Pressure drop in cross-flow zone
• Pressure drop in window zone
• Pressure drop in end zone

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Pressure Drop in Cross Flow Zone

• where ?Pi pressure drop calculated for an
  equivalent ideal tube bank
• Fb is bypass correction factor
• FL is leakage correction factor
• where jf is given by the following chart
• Ncv is number of tube rows crossed
• us is shell-side velocity

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Friction Factor for Cross Flow Banks
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Bells Method Bypass Correction Factor for
Pressure Drop

• a is 5.0 for laminar flow, Relt100
• 4.0 for transitional and turbulent flow, Regt100
• Ab is the clearance area between the bundle and
  shell
• Ns is the number of sealing strips encountered
  by bypass stream
• Ncv is the number of tube rows encountered in
  the cross- flow section

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Bells Method Leakage Factor for Pressure Drop

• where Atb is the tube to baffle clearance area
• Asb is the shell to baffle clearance area
• AL is total leakage area AtbAsb
• ßL is factor obtained from following
  chart

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Coefficient for FL
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Pressure Drop in Window Zones

• where us is the geometric mean velocity
• uw is the velocity in the window zone
• Ws is the shell-side fluid mass flow
• Nwv is number of restrictions for cross-flow in
  window zone, approximately equal to the number of
  tube rows.

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Pressure Drop in End Zones

• Ncv is the number of tube rows encountered in the
  cross-flow section
• Nwv is number of restrictions for cross-flow in
  window zone, approximately equal to the number of
  tube rows.

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Bells Method Total Shell-side Pressure Drop
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Effect of Fouling

• Above calculation assumes clean tubes
• Effect of fouling on pressure drop is given by
  table above

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Condensers

• Construction of a condenser is similar to other
  shell and tube heat exchangers, but with a wider
  baffle spacing
• Four condenser configurations
• Horizontal, with condensation in the shell
• Horizontal, with condensation in the tubes
• Vertical, with condensation in the shell
• Vertical, with condensation in the tubes
• Horizontal shell-side and vertical tube-side are
  the most commonly used types of condenser.

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Heat Transfer Mechanisms

• Filmwise condensation
• Normal mechanism for heat transfer in commercial
  condensers
• Dropwise condensation
• Will give higher heat transfer coefficients but
  is unpredictable
• Not yet considered a practical proposition for
  the design of condensers
• In the Nusselt model of condensation laminar flow
  is assumed in the film, and heat transfer is
  assumed to take place entirely by conduction
  through the film.
• Nusselt model strictly applied only at low liquid
  and vapor rates when the film is undisturbed.
• At higher rates, turbulence is induced in the
  liquid film increasing the rate of heat transfer
  over that predicted by Nusselt model.

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Condensation Outside Horizontal Tubes

• where (hc)1 is the mean condensation film
  coefficient, for a single tube
• kL is the condensate thermal conductivity
• ?L is the condensate density
• ?v is the vapour density
• µL is the condensate viscosity
• g is the gravitational acceleration
• G is the tube loading, the condensate flow per
  unit length of tube.
• If there are Nr tubes in a vertical row and the
  condensate is assumed to flow smoothly from row
  to row, and if the flow is laminar, the top tube
  film coefficient is given by

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Condensation Outside Horizontal Tubes

• In practice, condensate will not flow smoothly
  from tube to tube.
• Kerns estimate of mean coefficient for a tube
  bundle is given by
• L is the tube length
• Wc is the total condensate flow
• Nt is the total number of tubes in the bundle
• Nr is the average number of tubes in a vertical
  tube row
• For low-viscosity condensates the correction for
  the number of tube rows is generally ignored.

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Condensation Inside and Outside Vertical Tubes

• For condensation inside and outside vertical
  tubes the Nusselt model gives
• where (hc)v is the mean condensation coefficient
• Gv is the vertical tube loading, condensate per
  unit tube perimeter
• Above equation applicable for Relt30
• For higher Re the above equation gives a
  conservative (safe) estimate.
• For Regt2000, turbulent flow situation analyzed
  by Colburn and results in following chart.

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Colburns Results
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Boyko-Kruzhilin Correlation

• A correlation for shear-controlled condensation
  in tubes simple to use.
• The correlation gives mean coefficient between
  two points at which vapor quality, x, (mass
  fraction of vapour) is known.
• 1,2 refer to inlet and outlet conditions
  respectively
• In a condenser, the inlet stream will normally be
  saturated vapour and vapour will be totally
  condensed. For these conditions

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Flooding in Vertical Tubes

• When the vapor flows up the tube, tubes should
  not flood.
• Flooding should not occur if the following
  condition is satisfied
• where uv and uL are velocities of vapor and
  liquid and di is in metres.
• The critical condition will occur at the bottom
  of the tube, so vapor and liquid velocities
  should be evaluated at this point.

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Condensation Inside Horizontal Tubes

• When condensation occurs, the heat transfer
  coefficient at any point along the tube will
  depend on the flow pattern at that point.
• No general satisfactory method exists that will
  give accurate predictions over a wide flow range.

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Two Flow Models

• Two flow models
• Stratified flow
• Limiting condition at low condensate and vapor
  rates
• Annular flow
• Limiting condition at high vapor and low
  condensate rates
• For stratified flow, the condensate film
  coefficient can be estimated as

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• Condensation of steam
• For air-free steam a coefficient of 8000 W/m2-0C
  should be used.
• Mean Temperature Difference
• A pure, saturated, vapor will condense at a
  constant temperature, at constant pressure.
• For an isothermal process such as this, the LMTD
  is given by
• where Tsat is saturation temperature of vapor
• t1 (t2) is the inlet (outlet) coolant
  temperature
• No correction factor for multiple passes is
  needed.