Monday, March 19, 2018

## Heat Exchanger Design

Goals:

• Role of heat exchangers in chemical processing
• Basic concepts and terminology
• Types of heat exchangers
• Design methodology
• Sizing
• Design
• Rating

Purpose of a Heat Exchanger

• To heat or cool a stream flowing from item of equipment to another. The steam may be a
• A liquid
• A gas
• A multiphase mixture
• To vaporize a liquid stream
• To condense a vapor stream

Single Tube Pass, Single Shell Pass CounterCurrent Heat Exchanger

Types of Heat Exchanger Service

• Fluid heated by external utility
• Steam
• Hot oil or molten salt
• Combustion gas (furnace)
• Electricity (resistive, inductive, microwave)
• Fluid cooled by external utility
• Cooling water
• Refrigeration
• Fluid heated or cooled by other process stream

Calculations of Cooling Curves

• Sensible heat: $Q=WC_{\text{p}}(T_{\text{in}}-T_{\text{out}})$

(For constant Cp: $Q=W(H_{\text{in}}-H_{\text{out}})$ otherwise)

• Latent Heat: $Q=W\lambda$
• Multicomponent Cooling Curves: Requires point-by-point flash calculations

Feasible Cooling Curve Pairings

• Corollary of the Second Law of Thermodynamics

Heat can only be transferred from a higher temperature to a lower one.

• For heat exchangers this means that the higher temperature cooling curve and the lower temperature heating curve cannot intersect.
• When this condition is satisfied, the pairing of a heating and cooling curve is said to be feasible.

Maximum Heat Exchanger Duty

• Qmax, the maximum amount of heat that can be transferred in a heat exchanger, no matter how large it is, occurs when the heating and cooling curves either,
• Intersect at one end of the exchanger or the other or
• Become tangent within the exchanger
• For sensible heating with constant fluid heat capacities, the curves are straight lines. They will intersect at that end of the exchanger whose entering fluid has the largest WCp, caiit it Wcpmax.

Maximum Duty Qmax

• For WCp>WCp2, the exchanger will “pinch: at the Fluid 1 inlet.

$Q_{\text{max}}=WC_{\text{p}}2(T1_{\text{in}}-{T2_{\text{in}})$

• For WCp2>WCp1 the exchanger will “pinch” at the Fluid 2 inlet (as in the previous diagram)

$Q_{\text{max}}=WC_{\text{p}}1(T1_{\text{in}}-{T2_{\text{in}})$

Basic Performance Equations For a Heat Exchanger

For the fluid flowing in the positive z direction an energy balance on the section dz gives

$dT1/dz=(Ua./WC_{\text{p}})(T2-T1)$

where   U = the overall heat transfer coefficient and

a= the heat transfer area per unit length

if the second fluid is a pure component either vaporizing or condensing, them

$dT2/dz=0$

Case 1: if the second fluid is a pure component either vaporizing or condensing, then

$dT2/dz=0$

Case 2: if the second fluid is flowing in the negative z direction, i.e., in countercurrent flow, and energy balance on the section dz gives

$dT2/dz=(Ua./WC_{\text{p}}(T2-T1)$

Rating Solution for Case1

$T1(z)=Exp[-\upeta1 \ z]T1(0)+(1-Exp[-\upeta1 \ z])T1$

Where $\upeta1=U\ a\ /WC_{\text{p}}1$

For z = L, A = aL and $N1=UA/WC_{\text{p}}1$ where N1 is defined as the number of heat transfer units (NTU’s) with respect to fluid 1. Let T1out = T1(L) and T1in = T1(0).

Then

$T1_{\text{out}}=Exp[-N1]T1_{\text{in}}+(1-Exp[-N1])T2$

The exchanger efficiency {tex inline}E=(T1_{\text{out}}-T1_{\text{in}}/(T2-T1_{\text{in}}){\tex}

$E = 1-Exp[-N1]$

Design Solution for Case 1

$N1 = -UA/WCp1 = ln \{1 – E\}$

$= ln \{[T2 – T1_{\text{out}}/T2 – T1_{\text{in}}]\}$

Note that $Q = WC_{\text{p}}1(T1_{\text{out}} – T1_{\text{in}})$

Substituting and rearranging gives

$Q = UA\ LMTD$

Where

$LMTD={{[(T2-T1_{\text{out}})-(T2-T1_{\text{in}}]} \over {ln{\{[T2-T1_{\text{out}}]/[T2-T1_{\text{in}}]}{\}}}}$

which is the well-known heat exchanger design equation.

Rating Solution for Case 2

Without going through the details:

$T2_{\text{out}}={{[Exp(N2-N1)-1] T1_{\text{in}}+[1-N1/N2] T2_{\text{in}}} \over{Exp(N2-N1)-N1/N2]}}$

where

$N1 = UA/WC_{\text{p}}1$

$N2 = UA/WC_{\text{p}}2$

$T1_{\text{out}}={Exp(N2-N1)[1-N1/N2] T1_{\text{in}} \over {Exp(N2-N1)-N1/N2]}} + {{N1/N2[Exp(N2-N1)-1] T2_{\text{in}}} \over {[Exp(N2-N1)-N1/N2]}$

Design Solution For Case 2

The design solution is essentially the same for Case 2 as for Case 1, namely,

$Q=UA\ LMTD$

where now $LMTD={{(T2_{\text{out}}-T1{\text{in}})-(T1_{\text{out}}-T2_{\text{in}})} \over {ln\{(T2_{\text{out}}-T1_{\text{in}})/(T1_{\text{out}}-T2_{\text{in}})\}}$

Reprise: Assumptions

• The Cp's are constant over the temperature range involved. (Reasonable for most exchangers of practical interest.)
• U is constant over the temperature range involved. (Reasonable for most exchangers of practical interest.)
• Flow is pure countercurrent or pure cocurrent. If not, a correction factor F is required to adjust the LMTD.

$Q=UA\ F\ LMTD$

F has been derived for most common heat exchanger configurations (multiple tube passes, cross flow, etx.).

Rating Calculations

• If U and A are known along with the W's and Cp's, use the appropriate performance equations solutions.
• If only the specifications of the exchanger (number of tubes, length of tubes, tube diameter, baffle spacing, baffle cut, etc.) are given, compute A from the geometry and U from

$1/U = 1/hf1+1/hwall+1/hf2+rfouling$

using the appropriate correlations for hf1 and hf2

Sizing Calculations

• Choose a typical value for U based on the type of service. [Tables of typical values can be found most textbooks on heat exchanger design.]
• Determine the outlet temperatures based on the performance specifications and the appropriate energy balances.
• Calculate A from $Q=U\ A\ LMTD$

Rigorous Design

• Determine the basic heat exchanger features such as tube diameter and wall thickness, tube length, baffle spacing, and baffle cut.
• Estimate the area required based on sizing calculation.
• Determine the number of tubes required to provide the estimated area. Check the tube-side fluid velocity. If below the acceptable range, estimate number of tube passes required.
• Calculate U based on the appropriate correlations and a reasonable estimate of the fouling resistance.
• Iterate until Uassumed = Ucalculated.
• Check the pressure drops and adjust design if unacceptable.

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