AGITATED VESSEL HEAT TRANSFER

Carpenter, K.J.
DOI: 10.1615/AtoZ.a.agitated_vessel_heat_transfer

Introduction
Heat transfer in agitated vessels can be carried out either through an external jacket on the vessel or by
internal coils. Where a jacket or coils cannot provide the surface area required, a recirculation loop
with an external heat exchanger may be used. In this case the heat exchanger would be designed by the
normal methods and will not be covered further in this chapter. (See Heat Exchangers.)
A jacket may be either a full conventional jacket, a dimpled jacket, or a half-pipe jacket, often called a
limpet coil, as illustrated in Figure 1a, Figure 1b and Figure 1c. The designs are compared by
Markovitz (1971).

Figure 1.
A conventional jacket has the advantage that it covers the full wall and base surface and is very simple
to construct. A dimpled jacket allows construction from light gauge metals while maintaining strength.
A half-pipe jacket may be cheaper for a high pressure on the service side and has the advantage that
more than one service can be supplied to different sections of the wall. However, a limited amount of
the surface will be covered by a half-pipe jacket, the large amount of weld can cause mechanical
concerns where thermal cycling occurs and the jacket welding must be spaced from the dished end
main welds to maintain mechanical integrity of the vessel wall.
Internal coils may be full helical coils, or a number of smaller, ringlet coils. Figure 2a and b.

Figure 2.
A full helical coil is the more usual design, allowing the maximum surface to be installed, but requires
a two-piece vessel with a relatively expensive main flange. Smaller ringlet coils can be designed to be
inserted through large branches on the upper vessel dished end, but can leave quiescent, unmixed
regions within their circumference.
The choice between a jacket and coils is based on a number of considerations. For highly corrosive or
highly reactive materials, a jacket has the advantage that there are no extra materials of construction
and no extra metal surface in contact with the process other than the normal vessel wall. There is also
less risk of cooling fluid coming into contact with the reaction mass. For the manufacture of
pharmaceuticals, fine chemicals and performance products, a jacket minimizes contamination as there
are no extra surfaces to clean. For materials with difficult rheology the full range of agitator designs
can be used with a jacket without difficulty. However, a jacket has a lower heat transfer performance
than a coil as there will be a lower process side coefficient, usually a greater wall thickness, and a
smaller surface area. A jacket may also require a higher service side flow. For exothermic reactions, a
jacketed vessel has the disadvantage that the area/volume ratio decreases with increasing scale. The use
of a greater height/diameter ratio at larger scale can help to reduce this problem, but only to a limited
extent. A coil has the advantage that a large surface area can be provided, for example, in one particular
highly exothermic reaction 18 m2m−3 has been installed in a 5 m3 reactor. However, it is important not
to pack the coil so tightly as to form a false wall.
Agitated vessel heat transfer is commonly used in batch manufacture where it is frequently necessary to
calculate the time to heat or cool a batch or the cooling capacity required to hold an exothermic or
endothermic reaction at constant temperature. It may also be necessary to define the stable operating
region or acceptable reagent addition rate for an addition controlled highly exothermic semi-batch
reaction. The heat removal rate is defined by:
(1)

For the simple case of the time to cool or heat a batch of mass, M:
(2)

For a constant service side temperature, Ts, for example, steam heating:
(3)

The time to reach a temperature, T from a starting temperature Tt=0 is:

(4)

For more complex situations numerical integration may be required, but there are many suitable
dynamic simulation languages available. For coils and jackets, the Overall Heat Transfer Coefficient
can be calculated in the usual way:
(5)

where α and αs are the process and service side heat transfer coefficients, respectively. The service side
fouling resistance, l/αf, will be available from local experience or from Kern (1950) , for example. As a
general guide, approximate overall coefficients typical of agitated jacketed vessels are given in Tables 1
and 2.
Table 1. Typical overall coefficients for jacketed glass lined steel vessels
Duty U (W m−2K−1)
Distillation/Evaporation 350
Heating 310
Cooling 200
Cooling (chilled service) 100
Table 2. Typical overall coefficients for jacketed carbon and stainless steel vessels
Duty U (W m−2K−1)
Heating 400
Cooling 350
Cooling (chilled service) 150
A typical overall coefficient for a well designed coil would be 400 to 600 Wm2K−1.

Service heat transfer coefficient

Under normal circumstances the overall coefficient should be dominated by the process side. However,
for the service side the following guidelines should be observed to ensure good performance:
For jackets:
1. A conventional jacket should be fitted with baffles (see Figure 1a).
2. Service injection nozzles should be used to direct the service flow, especially for a glass-lined
steel vessel (see Figure 3).
3. A vent should be fitted and maintained to prevent gas blanketing.
4. For a plain jacket with liquid service the target circumferential velocity should be 1-1.5 ms −1.
5. For a half-pipe jacket with liquid service the minimum target velocity should be 2.3 ms−1.
6. For a dimpled jacket with liquid service, pressure drop may limit the velocity to 0.6 ms −1.

Figure 3. Service injection nozzle.

For an internal coil:
1. For a liquid service, the minimum target velocity should be 1.5 ms−1.
There are several correlations available for the service side coefficient, depending on the jacket or coil
design and the flow regime of the service fluid. Fletcher (1987) provides some useful guidance and the
research club, HTFS has also produced a design report for members. The following correlations are
recommended:
1. Conventional unbaffled jacket, liquid service with high flow [(Lehrer (1970)]
(6)

where:
(7)

vi is the velocity at the inlet nozzle or branch and vB is the velocity component due to buoyancy,
Dj is the jacket diameter and DT is the vessel diameter.
(8)
 where is the volumetric flow rate, di is the diameter of the inlet, z is the wetted
height of the jacket, β is the fluid thermal expansion coefficient, and ΔTs is the temperature rise
of the service fluid. VA is the rise velocity in the jacket annulus and depends on the inlet
orientation:
(9)

2. Conventional unbaffled jacket, liquid service with high flow [(Lehrer (1970)] (see also Free
Convection)
(10)

Here,
K = 0.15 for upward flow, heating; downward flow cooling;
K = 0.128 for downward flow heating; upward flow cooling;
ΔTm is the mean temperature difference between the service and the vessel
wall
(11)

3. Baffled or dimpled jacket, liquid service. The service side coefficient for a baffled or dimpled
jacket will be greater than for an unbaffled jacket with high flow, therefore the above can be
used as a conservative estimate. Using the correlation for a half-pipe coil with the flow area
equivalent to the baffle channel is not recommended as it may give an overestimate.
4. Half-pipe coil, liquid service
(12)

This is the normal Sieder-Tate equation, (see Forced Convective Heat Transfer) applied to the
whole jacketed area with the effectiveness factor (E) from Kneale (1969), typically 0.8–1. Nu
and Re are based on the hydraulic mean diameter, de:
(13)

5. Condensing service. A condensing coefficient in a jacket should be extremely high compared

to the process side and normally αs−1 ~ 0. A conservative estimate can be obtained from the
Nusselt analysis [see Kern (1950)]:
(14)
 The physical properties refer to the liquid phase and ΔT = Tsat - Twall (see Condensation).

Process side heat transfer coefficient

The process side coefficient will be determined by the agitator type and speed. (See also Agitation
Devices.) For low viscosity fluids, most turbine-type high-speed agitators can give good performance.
For high viscosity and Non-Newtonian Fluids, larger diameter agitators will be required. Harnby et al.
(1985) and Oldshue (1983) provide guidance on agitator selection. For Non-Newtonian Fluids, there
are two important considerations:
1. A mean apparent viscosity is required to calculate Nu from Re. The normal practice is to
estimate it using the Metzner-Otto approach, where:
(15)

Kmo depends on the agitator type, N is the rotational speed (s -1).

The viscosity correction only allows for the effect of temperature near the wall and NOT the
distribution of shear rate. It will normally be sufficient to assume an homogeneous distribution
of shear rate. Calculation of a wall shear rate to predict a local ηa is beyond the scope of this
article.
2. It is essential to ensure that a material with a significant yield stress is maintained fluidized right
up to the vessel wall. Nienow (1988) reviews the design techniques. Use the vessel diameter
(DT) as the diameter of the region to be fluidized:
(16)

Po is the impeller Power number [Harnby et al. (1985)], and:

(17)

For the vessel wall surface, the process side coefficient can be calculated from:
(18)

(19)

For transfer to an internal coil:

(20)
Table 3. Metzner-Otto constants for impellers
Impeller type Kmo
propeller 10
disc or flat blade turbine 11.5
angled turbine 13
anchor 25*
helical ribbon 30
EKATO Intermig (0.8 DT) 40
*The value for an anchor depends on the rheology of the material, for more detail see Nienow
(1988).
Table 4. Heat transfer constants for impellers
Impeller A B
propeller 0.46 1.4
45° turbine 0.61 1.4
disc turbine 0.87 1.4
retreat curve 0.33 0.87
anchor 0.33
Intermig 0.54