Question

A shell and-tube heat exchanger is required for the following service:

	Hot stream	Cold Stream
	Aromatic Stream	Cooling Water
inlet Temperature (oC)	85	20
outlet Temperature (oC)	40	35
Mass Flowrate x heat Capacity (kW/oC)	85.2

	Hot Stream	cold stream (Cooling water)
Heat Capacity (J/kg K)	2840	4193
Density (kg/m3)	750	999
Viscosity (cP)	0.34	1.016
Thermal conductivity (W/m.K)	0.19	0.594
Fouling Factor (m2.oC/W	0.00018	0.000176

? The cooling water is allocated to the tube-side of the exchanger.
? It is preferable to employ a fixed-tubesheet heat exchanger for the service.
? 25.4 mm OD tubes (2.1 mm wall thickness) on a 1.25 x OD triangular pitch are available. The
thermal conductivity of the tube material is kw = 51 W/m?K.
? Consider four (4) tube passes.
? The maximum tube length that can be employed is 6.098 m i.e. L < or = 6.098 m
? Assume 1-shell pass. The shell diameter should not exceed 1.5 m i.e. Ds < or = 1.5 m
? Baffle cut is set at 25% and the baffle spacing (lb) is assumed to be 0.5 x Ds
? The maximum allowable tube-side and shell-side pressure drops are 70 kPa and 50 kPa
respectively.
? Total annual cost (TAC) is given as follows:
TAC = 123 A^(0.59) + 1.31 [ delta P_{tube .} m_tube/ density_tube + delta P_{shell .} m_shell/ density_shell ]
where A is the area of the exchanger in m², TAC is in $/year, ?delta P is in Pa, m in kg/s and density? in
kg/m3

2.2 Provide a mathematical expression for the following constraints:
o the tube side velocity,
o the shell-side velocity, and
{Hint: Note: cooling water in the tubes}

2.3 Derive an expression for the number of tubes in terms of the tube-side velocity, number of tube
passes, mass flowrate and tube inside diameter.

2.4 Calculate the number of tubes at the minimum and maximum tube-side velocities
2.1). Show the calculations and summarise your answers in a table.
{It is convenient to use a spreadsheet for this calculation}

2.5 For each of the number of tubes calculated in 2.4, determine the shell diameter Ds. (you can fit a straight
line to the data if you would rather like to use an equation). Show the calculations and summarise
your answers in a table.

2.6 Plot a graph of tube length vs shell diameter for the minimum and maximum velocity as well as
the maximum shell diameter. Discuss your findings.

2.7 Select various shell diameters between the limits found in Coulson. {4 to 5 values should be sufficient}.
For each shell diameter, determine the tube length at the maximum tube-side pressure drop.
Show the calculations and summarise your answers in a table.

2.8 Using the same shell diameters selected in 2.7, determine the tube length at the maximum shellside
pressure drop. Show the calculations and summarise your answers in a table.
2.9 For each shell diameter, determine the tube length based on the heat transfer duty i.e. Q=UA?Tm
{You need to determine the heat transfer coefficients on the tube and shell-side}. Show the
calculations and summarise your answers in a table.
2.10 Plot your results from 2.7, 2.8 and 2.9 on a graph of tube length (x-axis) vs shell diameter (yaxis).
{Please use a spreadsheet to do this. Do not submit hand-drawn plots}. Identify the feasible
region.
2.11 Determine the exchanger with the minimum cost. Discuss your approach and findings.
2.12 How does the above approach of exchanger design compare/contrast with the standard
method?

Answer 1

A-2.4)

Ovrall HTC	600	W/m2K Taken from R c vol. 6
Tube ID (di)	19	mm
No. of Tube pass	4
Mass flow rate	30	kg/sec
Heat Transfer Area	260	m2
Tube Length	Tube Side velocity	No. of Tubes
1.83	0.237085	2381.437
2.44	0.316113	1786.077
3.66	0.474170	1190.718
4.88	0.632227	893.039
6.1	0.790283	714.431

A-2.5

Tube Length	Tube Side velocity	No. of Tubes	Tube Bundle Dia	Clearance	Shell Dia
1.83	0.237085	2381.437	1636.5790	NA	-
2.44	0.316113	1786.077	1442.9763	80	1522.9763
3.66	0.474170	1190.718	1208.3568	77	1285.3568
4.88	0.632227	893.039	1065.4116	73	1138.4116
6.1	0.790283	714.431	966.2867	71.5	1037.7867

WHere k1=0.175 & N1=2.285 for 4 passes at tube side

FOr Tube bundle shell clearance refer graph 12.10 and for tune bundle dia refer table no. 12.4 of RC vol.6