C i Af (Cexc Cpump,T ) Cpump,s ) 

min 

max

c mt e

Af [(Ca Cb A ) (Ce Cf ( ΔPt )  ) (34) 

t t t (40) 

min max

t

(Ce Cf (   s ΔPs )e )]

s

where Cexc, Cpump,t and Cpump,s are the capital costs for the exchanger, tube side and shell side pumps, respectively。 

1

s s  s (41) 

High velocities will give high heat transfer coef- ficients but also a high pressure drop。 The velocity  must be high enough to prevent any suspended so- lids settling, but not so high as to cause erosion。 High velocities will reduce fouling。 Plastic inserts are some- timesused to reduce erosion at the tube inlet。  Typical 

design velocities are given below [15]。 

Cod 

(  mt ΔP  ms ΔP )C H

                           (35) 

Liquids。 Tube-side, process fluids: 1 to 2     m/s, 

t s

Ctot  Ci  Cod                                                                   (36) This new cost calculation is used in case study 3 

to have a same basis for comparison of performance of SA approach and GA approach。 

maximum 4 m/s if required to reduce fouling;  water:  1。5 to 2。5 m/s; shell-side: 0。3 to 1 m/s。 

Vapors。 For vapors, the velocity used will de- pend on the operating pressure and fluid density; the lower values in the ranges given below will apply to  high  molecular  weight  materials;  vacuum:  50  to 70 

m/s; atmospheric pressure: 10 to 30 m/s; high pres- sure: 5 to 10 m/s。 

In this work, the following constraints were im- posed on objective function: 

where x is the vector of optimization variables (Table 1)。 The set of constraints g(x) corresponds to the  inequalities given by Eqs。 (37)–(43)。 

For  implementation  of  the  SA  algorithm,    we 

used a penalty function in the objective function, to 

1 vt  2 m/s and 0。3 vs

Service constraints 

1 m/s

provide the following objective function to be mini- mized [16]。 

The hydraulic requirements of the service are  represented by upper bounds on the pressure drop of both streams: 

Obj (x ) Ctot (x ) penalty(x ) (44) 

The penalty function accounts for the violation of the constraints such that: 

ΔP  ΔPmax                                                                                                                     (42)