Heat Exchanger Rating (Bell-Delaware Method)

Heat Exchanger Rating (Bell-Delaware Method)

Stream Analysis Heat Exchanger

In Bell Delaware method, the fluid flow in the shell is divided into a number of individual streams. Each of these streams introduces a correction factor which is used to correct heat transfer coefficient and pressure drop across the shell. This article gives step-by-step guidance on doing heat exchanger rating analysis based on Bell-Delware method.

Shell Side Heat Transfer Coefficient, hs

Cross flow area, Sm is the minimum flow area in one baffle space at the center of the tube bundle. It is calculated by following equation:

Sm = B[(Ds - DOTL) + (DOTL - Do)(PT - Do)/PT,eff ]

where, PT is tube pitch, B is central baffle spacing, DOTL is outer tube limit diameter, Ds is shell diameter and Do is tube outside diameter.

PT,eff = PT for 30° and 90° layouts 
PT,eff = 0.707*PT for 45° layout

Shell side cross flow mass velocity, GS is defined as:

GS = mS/Sm

where, mS is shell side mass flow rate. Shell side Reynolds number ReS is then calculated from

ReS = Do.GS / μS

where, μS is the shell side fluid dynamic viscosity at average bulk temperature.

Shell side Prandtl number PrS is calculated as following :

PrS = CP,SS / kS

where, CP,S is the shell side fluid specific heat and kS is the shell side fluid thermal conductivity.

Colburn j-factor for an ideal tube bank is defined as:
Colburn j-factor
where a1, a2, a3 and a4 are correlation constants listed below.
Correlation constants j factor
The ideal tube bank based coefficient is calculated from –
ideal heat transfer coefficient
where, μS,W is shell side fluid viscosity at wall temperature.

Correction factor for Baffle Window Flow, JC

The factor JC accounts for heat transfer in the baffle windows. It has a value of 1.0 for exchanger with no tubes in the windows.

JC = 0.55 + 0.72FC 
FC = 1 - 2FW 
FW = (θCTL - Sin(θCTL))/2π 
θCTL = 2cos-1(Ds(1 - 2*Bc/100)/DCTL) 

where, Bc is segemental baffle cut in %.

Correction factor for Baffle Leakage, JL

The correction factor JL considers the effects of the tube-to-baffle and shell-to-baffle leakage streams on heat transfer.

JL = 0.44(1-rS) + (1-0.44(1-rS))exp(-2.2rL)
rS = Ssb /(Ssb + Stb) 
rL = (Ssb + Stb)/ Sm 
Ssb = Ds*DSB(π - 0.5θDS) 
Stb = (π/4)((Do+LTB)2 - Do2)Nt(1-FW)
θDS = 2cos-1(1 - 2Bc/100)

where, Nt is number of tubes, DSB is diametral clearance between shell & baffle and LTB is diametral clearance between tube and baffle.

Correction factor for Bundle Bypass effects, JB

Bundle bypass correction factor JB accounts for the bundle bypass stream flowing in the gap between the outermost tubes and the shell. The number of effective rows crossed in one cross flow section, Ntcc between the baffle tips is provided by following equation.

Ntcc = (Ds/Pp)(1 - 2Bc/100) 
Pp = PT 30.5/2 for 30° layout 
Pp = PT / 20.5 for 45° layout 
Pp = PT for 90° layout

Ratio of sealing strips to tube rows rss is provided by

rss = Nss/ Ntcc

where Nss is number of sealing strips (pairs) in one baffle.

The bundle bypass flow area, Sb is defind as

Sb = B(Ds - DOTL - Do/2)

where, B is central baffle spacing. Correction factor JB is then calculated as following –

JB = exp(-Cj(Sb / Sm)(1 - (2rss)1/3)) for rss < 0.5 
JB = 1 for rss >= 0.5 
Cj = 1.35 for ReS < 100 
Cj = 1.25 for ReS >= 100

Correction factor for adverse temperature gradient, JR

The factor JR accounts for the decrease in the heat transfer coefficient with downstream distance in laminar flow.

Ntcw = (0.8/Pp)(Ds(Bc/100) - (Ds-(DOTL-Do))/2 )
NB = 1 + (int)(L - 2Ls - LBIn - LBOut)/B 
NC = (Ntcw + Ntcc)(1 + NB) 
JRL = (10/NC)0.18 
JR = 1, ReS > 100 
JR = JRL + (20-ReS)(JRL - 1)/80, ReS <= 100, ReS > 20 
JR = JRL, ReS <= 20

where, L is tube length, Ls is tubesheet thickness, LBIn is inlet baffle spacing and LBOut is outlet baffle spacing.

Correction factor for unequal baffle spacing, JS

n1 = 0.6, ReS >= 100 
n1 = 1/3, ReS < 100 
JS = ((NB-1)+(LBIn/B)1-n1 + (LBOut/B)1-n1)/((NB-1)+(LBIn/B) + (LBOut/B))

Shell side heat transfer coefficient is calculated as

hs = hIdeal(JC.JL.JB.JS.JR)

Shell Side Pressure Drop, ΔPs

Friction factor for ideal tube bank is calculated as following –
friction factor for ideal tube bank
where b1, b2, b3 and b4 are correlational constants listed below.
friction factor constants
Pressure drop for an ideal tube bank is calculated from

ΔPIdeal = 2f(GS²/ρS)(μSS,W)0.14 Ntcc

Correction factor for Baffle Leakage, RL

RL = exp(-1.33(1+rS)rLp) 
p = 0.8 - 0.15(1+rS)

Pressure drop for window section, ΔPW

Following terms are calculated as –

SWG = (Ds²/8)(θDS - Sin(θDS)) 
SWT = Nt.FW(πDo²/4) 
GW = mS/(Sm.SW)0.5 
DW = 4.SW /(π.Do.Nt.FW + θDS.Ds)

Pressure drop for laminar and turbulent flow is calculated.

ΔPW, Turb = NB.RL(2+0.6*Ntcw).GW²/(2.ρS)

pressure drop for laminar flow

ΔPW = ΔPW, Turb , ReS >= 100 
ΔPW = ΔPW,Laminar , ReS < 100

Correction factor for Bundle Bypass effect, RB

RB = exp(-Cr(Sb / Sm)(1 - (2rss)1/3)) for rss < 0.5 
RB = 1 for rss >= 0.5 
Cr = 4.5 for ReS < 100 
Cr = 3.7 for ReS >= 100

Correction factor for unequal baffle spacing, RS

n = 0.2, ReS >= 100 
n = 1.0, ReS < 100 
RS = 0.5((B/LBIn)2-n + (B/LBOut)2-n)

Pressure drop in Central Baffle spaces, ΔPC is defined as –

ΔPC = (NB - 1)ΔPIdeal.RL.RB

Pressure drop in entrance & exit baffle spaces, ΔPE is calculated as –

ΔPE = ΔPIdeal(1 + Ntcw/Ntcc).RB.RS

Shell side pressure drop is calculated as following –


Tube Side Heat Transfer Coefficient, ht

Reynold’s number and Prandtl number are calculated as following –

ReT = Di.v.ρtt 
PrT = Cp,tt/kt

where, Di is tube inside diameter, v is velocity, ρt is density, μt is viscosity, kt is thermal conductivity and Cp,t is specific heat for fluid on tube side.

For laminar flow, ReT < 2300, Sieder and Tate correlation is used for Nusselt’s nubmer.

Nu = 1.86(ReT.PrT.Di/Leff)1/3 
Leff = L - 2*Ls

For turbulent flow, ReT > 10,000, following equation developed by Petukhov-Kirillov can be used.

Nu = (f/2)ReT.PrT/(1.07+12.7(f/2)0.5(PrT2/3-1)) 
f = (1.58 ln(ReT) - 3.28)-2

For transient flow, Nusselt number can be interpolated from Nu Laminar & Nu Turbulent.

Heat transfer coefficient is calculated as following –

ht = Nu.(kt/Di)(μtt, w)0.14

Tube Side Pressure Drop, ΔPt

Tube side pressure drop is calculated by following equation –

ΔPt = (4.f.Leff.Np/Di + 4.Np)ρt.v²/2

where, Np is number of tube passes.

Overall Heat Transfer Coefficient, U

Resistance due to tube wall is calculated as following

Rtube = Do/(2.ln(Do/Di).ktube)

where, ktube is thermal conductivity of tube material. Overall clean heat transfer coefficient, UClean is calculated as per below equation

UClean = 1/(hS + Do/(Di.ht) + Rtube)

Overall dirty heat transfer coefficient, UDirty is calculated as per below expression

UDirty = 1/(1/UClean + fshell + ftube)

where, fshell & ftube are fouling factors for shell and tube side.

Heat transfer coefficient required, URequired is calculated as following

URequired = Q /(A x LMTDcorrected)

where, Q is heat duty, A is heat transfer area and LMTDcorrected is corrected logarithmic mean temperature difference.

Over Surface, % = (UClean/URequired - 1)*100 
Over Design,  % = (UDirty/URequired - 1)*100

Web based calculation available at CheCalc.com


Spreadsheet for Heat Exchanger Rating based on Bell-Delaware Method


18 Replies to “Heat Exchanger Rating (Bell-Delaware Method)”

  1. There is some criterion for the dynamic pressure(DensityxVelocity^2) in the nozzles in existing equipment.

  2. Very interesting. A real great job. I have one curiosity. How to compute the effect of baffle orientation? I mean, those correlations are for vertical baffle cuts. I’ve checked in HTRI, and if you use horizontal the baffle cuts, the Reynolds number will increase by about 12%, and shell heat transfer coefficient will increase by about 17%. Do you have the correlations for that correction? I know horizontal baffle cuts are unusual due to accumulation of solids, but I know one case of heat exchanger with this configuration.

  3. There is a discrepancy between the Excel spreadsheet calculation and the online website calculation. The shell-side h seems to be incorrect in the Excel spreadsheet.

      1. Nevermind again. There is definitely an error with the shell-side HT coefficient calculation in the Excel spreadsheet.

        1. JL was off — found discrepancy in G-K61: Diametral Shell-Baffle Clearance calculation. One website, it is an input, not a calculation – regardless, these numbers are what caused the biggest discrepancy. I am still looking for one more discrepancy that relates to Js.

  4. Hello, great job!
    But I have one question, my appologies if I’m wrong but shouldn’t this equation:
    NB = 1 + (int)(L – 2Ls – LBIn – LBOut)/(Bc/100)
    be this:
    NB = 1 + (int)(L – 2Ls – LBIn – LBOut)/(B) ?
    It makes more sense.

    1. Also you have it in spreadsheet as NB = 1 + (int)(L – 2Ls – LBIn – LBOut)/(B/100), but dividing B by 100 doesn’t make any sense. I believe you corrected Bc to B and then forgot to delete the 100?

  5. Is the equation for number of baffles “NB” correct?
    “Bc” in equation[NB = 1 + (int)(L – 2LS – LBin – LBout ) / (Bc/100)] is baffle cut %. I think that the center baffle spacing “LBc” is correct. Actually, “LBc” is using in spreadsheet. But the calculation for “NB” in this spreadsheet may be not correct,too. I think it is not “(Bc/100)” but “(LBc) in equation and it is not “LBc/100” but “LBc/1000”.

      1. Thank you for your reply. I undestand that abbrevation “B” means the central baffle spacing in this text. But the abbrevation of the central baffle spacing is “LBc” in spreadsheet. I think this is slightly confusing.

  6. One more comment. Is the equation for “Overall H.T.C Dirty (UDirty)” in spread sheet correct? Equation is [= 1/(1/Uclean + “Tube Side Fouling Factor” + “Shell Side Fouling Factor”)] I think there is no correction of tube diameter for the tube side fouling factor and it is not “Tube Side Fouling Factor” but “(Tube Side Fouling Factor) x (Do / Di)”.
    Anyway your information in this site was very useful for me. Thank you very much.

  7. I have one more question. Generally, the diamentral shell-baffle clearance DSB means the difference of shell inside diameter and baffle outside diameter. So half of DSB as the clearance of shell and baffle should be used for calculation of the shell to baffle leakage area SSB. If DSB is the diamental clearance, the equation for SSB may be not [Ds x DSB x ( PI() – 0.5 x θDS)] but [Ds x DSB / 2 x ( PI() – 0.5 x θDS)] . Do you think which is correct?

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