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ExxonMobil Proprietary MIXING OPERATIONS
HEAT TRANSFER IN AGITATED VESSELS DESIGN PRACTICES
Section
Page
XIII-F
1 of 16
December, 2001 Changes shown by ➧
CONTENTS Section
Page
SCOPE ............................................................................................................................................................2 REFERENCES.................................................................................................................................................2 BACKGROUND...............................................................................................................................................2 DEFINITIONS ..................................................................................................................................................2 HEAT TRANSFER SURFACE ARRANGEMENTS .........................................................................................2 JACKETS FOR UTILIZING THE VESSEL WALLS .................................................................................3 INTERNAL COILS ...................................................................................................................................3 HEAT TRANSFER CORRELATIONS AND DESIGN PROCEDURE ..............................................................3 PROCESS SIDE HEAT TRANSFER COEFFICIENTS............................................................................4 Turbines - Paddles (All Styles) .............................................................................................................4 SERVICE SIDE HEAT TRANSFER COEFFICIENT................................................................................6 SERVICE SIDE PRESSURE DROPS .....................................................................................................7 CALCULATION OF HEAT TRANSFER RATE ........................................................................................7 NON-NEWTONIAN FLUIDS ............................................................................................................................8 SAMPLE PROBLEM .......................................................................................................................................8 NOMENCLATURE.........................................................................................................................................10 FIGURES Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6
Conventional Jacket ..........................................................................................................12 Conventional Baffled Jacket ..............................................................................................13 Half-Pipe Jacket ................................................................................................................13 Dimple Jacket....................................................................................................................14 Typical Helical Coil Configuration......................................................................................15 Typical Baffle Coil..............................................................................................................16
Revision Memo 12/01
ExxonMobil Research and Engineering Company – Fairfax, VA
ExxonMobil Proprietary Section
MIXING OPERATIONS
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XIII-F
2 of 16
HEAT TRANSFER IN AGITATED VESSELS DESIGN PRACTICES
December, 2001
SCOPE This section covers heat transfer to or from the contents of agitated process vessels. The primary function of agitation in these vessels is mixing. Thus they are designed to satisfy a given mixing requirement. Heat transfer is considered a secondary requirement and is calculated for an already determined mixer configuration.
REFERENCES DESIGN PRACTICES Section IX Section XIV
Heat Exchange Equipment Fluid Flow
OTHER REFERENCES Edwards, M. F. and Wilkinson, W. L., Heat Transfer to Newtonian and Non-Newtonian Fluids in Agitated Vessels, HTFS - DR 27, Heat Transfer and Fluid Flow Service, AERE, Harwell, 1972. Uhl, V. W. and Gray, J. B., eds. Mixing-Theory and Practice, Vol. 1, Academic Press, 1966. Nagata, S., Mixing, Principles and Applications, Halsted Press, 1975.
BACKGROUND Frequently the contents of an agitated vessel must be heated or cooled to a given operating temperature by intentional heat transfer to or from the fluid in the vessel. Additionally, in some mixing situations, the mixing power dissipation to the fluid is high enough to cause a significant temperature increase. This may require a design, which includes intentional cooling. Since the vessels are actually designed for their mixing duties, the agitators used are those appropriate for this mixing. In general, agitators which force large amounts of fluid to circulate near the heat transfer surfaces provide the most efficient heat transfer. In the case of close proximity impellers used for high viscosity (> 5,000 cP or 5 Pa•s) mixing, heat transfer is promoted by the thinning of the amount of stagnant fluid near the wall. Typical clearance between impeller and tank wall is 1/2 in. (12.5 mm). Rubber scrapers can additionally be added to close proximity impellers to keep the wall surface free from deposits. The surface needed for heat transfer can take a variety of forms. For close proximity impellers, the vessel wall itself is used in conjunction with jacketing. For turbines and propellers, the vessel walls or internal coils can be used. The various arrangements in common use are discussed below.
DEFINITIONS The definitions given in Section XIII-A also pertain to this section.
HEAT TRANSFER SURFACE ARRANGEMENTS The commonly used heat transfer surfaces are the vessel walls, through the use of external jackets, and internal coils. In general, coils are preferred over jackets because of lower costs, higher operating pressures, and higher inside heat transfer coefficients. Coils are particularly suitable for low viscosity fluids in combination with impellers, which give high radial flows normal to the coils. On the other hand for high viscosity fluids, a close clearance impeller in a jacketed vessel is probably more effective. Also coils are unsuitable with process liquids that foul. For “standard geometry," coils have about the same heat transfer area as jackets. However, by increasing the helix diameter, decreasing the spacing between turns, or using concentric coils, the heat transfer area provided by coils can be increased. Since these changes in coil design restrict fluid circulation in the vessel and thus heat transfer coefficient, proportional increases in total heat transfer are not achieved. Tank baffling should be used for other than close proximity impellers as dictated by the mixing situation. For jacketed vessels, wall baffles should be used if the fluid viscosity is at any time less than 5000 cP (5 Pa•s). For vessels equipped with coils, wall baffles should be used if the clear space between turns is at least twice the OD of the coil tubing and the fluid viscosity is less than 1000 cP (1 Pa•s). Otherwise the baffles should be located inside of the coil helix.
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Section XIII-F
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HEAT TRANSFER SURFACE ARRANGEMENTS (Cont) JACKETS FOR UTILIZING THE VESSEL WALLS A typical full vessel side and bottom jacketing configuration is shown in Figure 1. For this configuration the heat transfer area is given by: A
=
æL ö + 0.268 ÷ èT ø
πT 2 ç
where: A T L
= = =
Eq. (1)
Heat transfer area, ft2 (m2) Vessel diameter, ft (m) Vessel straight side, ft (m)
For a given vessel volume, a higher L/T ratio results in higher surface area. For simpler configurations, the area can be directly calculated for the cylindrical or circular geometry involved. Conventional Jackets - A conventional jacket is shown in Figure 1. Spiral baffling within the jacket as shown in Figure 2 should be used. Conventional jackets are a good choice for small vessels (< 500 gal or 1.9 m3) and for vessels with high internal pressures (internal pressure > 2 x jacket pressure). They are not recommended for jacket pressures greater than 100 psi (680 kPa) or high temperatures. Half-Pipe Jackets - A typical half-pipe jacket is shown in Figure 3. They are useful for high pressures (up to 600 psi or 4082 kPa) especially when jacket pressure determines the vessel wall thickness. Half-pipe jackets are better for liquid than for vapor service fluid. They can be easily zoned so that only a portion of the heat transfer area is used. A 3 in. (76 mm) nominal pipe size is typically used for forming the jacket. For maximum heat transfer, the space between the half-pipe coils is 3/4 in. (19 mm). However, if the inside heat transfer film coefficient is low, the space between the half-pipe coils can be increased without significant loss in heat transfer surface. Dimple Jackets - A typical dimple jacket is shown in Figure 4. Such jackets are suitable for larger vessels, particularly when jacket pressure determines the vessel wall thickness (Pjacket/Pvessel > 0.6). They are satisfactory up to 300 psi (2041 kPa) and 700°F (371°C). High jacket pressure drops are encountered with liquid flows. Typically the dimples are on a square pitch of 2.5 in. (63.5 mm). External Electrical Heaters - The vessel wall can also be used as the heat transfer surface by placing external electrical heaters around the vessel. For small vessels, strap-on electrical heaters are available.
INTERNAL COILS Helical Coils - Helical coils are the most common type of coil. Typical layout and relative dimensions are given in Figure 5. The heat transfer area provided by a helical coil is given by:
A = π dc nt where: A dc nt Dc Sc
= = = = =
[ (π D ) c
2
+ (Sc + dc ) 2
]
1/ 2
Eq. (2)
Heat transfer area (process side), ft2 (m2) Coil tubing outside diameter, ft (m) Number of helical turns Coil helix diameter, ft (m) Open space between turns, ft (m)
Baffle Coils - A typical baffle coil is shown in Figure 6. They are less common than helical coils but they provide heat transfer area while also serving as baffles.
HEAT TRANSFER CORRELATIONS AND DESIGN PROCEDURE Heat transfer rates in agitated vessels have been correlated in a manner similar to that in conventional heat exchangers; namely, by the use of process side and service fluid side heat transfer coefficients. Correlations for the coefficients are normally given in terms of products of dimensionless groups and are basically empirical fits of experimental data. The correlations given below are from literature sources and are believed to be reliable. However, they have not been validated by ExxonMobil operating or laboratory data.
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HEAT TRANSFER IN AGITATED VESSELS DESIGN PRACTICES
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HEAT TRANSFER CORRELATIONS AND DESIGN PROCEDURE (Cont) PROCESS SIDE HEAT TRANSFER COEFFICIENTS The nomenclature used in all of the following Eqs. (3) through (14) is: C
=
Impeller elevation (to center of impeller) above bottom of vessel, ft (m)
Cp D Dc dc
= = = =
Fluid heat capacity, Btu/lb°F (J/kg°C) Impeller diameter, ft (m) Diameter of coil helix, ft (m) Outside diameter of tube coil, ft (m)
hc
=
Heat transfer coefficient, vessel fluid to coil wall, Btu/(hr•ft2•°F) (W/m2°C)
hj i
= =
Heat transfer coefficient, vessel fluid to jacket wall, Btu/(hr•ft2•°F) (W/m2°C) Number of impellers
k N nb np T w Z
= = = = = = =
Thermal conductivity, Btu/(hr•ft2•°F/ft) (W/m°C) Impeller rotational speed, rpm (rps) Number of baffles Number of blades on turbine impeller Vessel diameter, ft (m) Blade width of impeller in direction parallel to axis of rotation, ft (m) Fluid depth in vessel, ft (m)
θ
=
Turbine blade angle from horizontal, °
µ
=
Fluid viscosity at bulk temperatures, lb/(ft•hr) (Pa•s*)
µw
=
Fluid viscosity at wall temperature, lb/(ft•hr) (Pa•s*)
ρ
=
Fluid density, lb/ft3 (kg/m3)
The physical properties used are those of the process fluid. * Viscosity in Pa•s is obtained by multiplying viscosity in centipoises by 10-3. Turbines - Paddles (All Styles)
1.
Unbaffled
For jackets: h jT k
æ D2 N ρ ö ÷ = 0.525 ç ç µ ÷ è ø
2/3
æ Cp µ ö ç ÷ ç k ÷ è ø
1/ 3
æ µ ç çµ è w
ö ÷ ÷ ø
0.14
æDö ç ÷ èTø
− 0.25
æwö ç ÷ èTø
0.15
æCö np0.15 ç ÷ èZø
0.15
(sin θ) 0.5
Eq. (3)
For helical coils with the impeller inside the coil array: hc T = 0.825 k
æ D2 N ρ ö ç ÷ ç µ ÷ è ø
0.56
æ Cp µ ö ç ÷ ç k ÷ è ø
1/ 3
æ µ ç çµ è w
ö ÷ ÷ ø
0.14
æDö ç ÷ èTø
− 0.25
æwö ç ÷ èTø
0.15
np
0.15
æ dc ö ç ÷ è T ø
− 0.3
Eq. (4)
For helical coils with the impeller below the coil array: hc T = 1.05 k
æ D2 N ρ ö ç ÷ ç µ ÷ è ø
0.62
æ Cp µ ö ç ÷ ç k ÷ è ø
1/ 3
æ µ ç çµ è w
ö ÷ ÷ ø
0.14
æDö ç ÷ èTø
−0.25
æwö ç ÷ èTø
0.15
æD ö np0.15 ç c ÷ è T ø
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Eq. (5)
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HEAT TRANSFER CORRELATIONS AND DESIGN PROCEDURE (Cont) 2.
Baffled
(4 baffles except as included in correlation for baffle coils) For jackets: æ D2 N ρ ö ÷ = 1.40 ç ç µ ÷ k è ø
h jT
2/3
æ Cp µ ö ç ÷ ç k ÷ è ø
1/ 3
æ µ ç çµ è w
ö ÷ ÷ ø
0.14
æDö ç ÷ èTø
−0.3
æwö ç ÷ èTø
0.45
æCö np0.2 ç ÷ èZø
0.2
æZö ç ÷ èTø
− 0.6
(sin θ) 0.5
Eq. (6)
For helical coils: hc T = 2.68 k
æ D2 N ρ ö ç ÷ ç µ ÷ è ø
0.56
1/ 3
æ Cp µ ö ç ÷ ç k ÷ è ø
æ µ ç çµ è w
ö ÷ ÷ ø
0.14
æDö ç ÷ èTø
− 0.3
æwö x ç ÷ èTø
0.3
æCö np0.2 ç ÷ èZø
0.15
æZö ç ÷ èTø
− 0.5
(sin θ) 0.5 Eq. (7)
For baffle coils: hc dc = 0.10 k
æ D2 N ρ ö ç ÷ ç µ ÷ è ø
0.65
æ Cp µ ö ç ÷ ç k ÷ è ø
1/ 3
æ µ ç çµ è w
ö ÷ ÷ ø
0.14
æDö ç ÷ èTø
1/ 3
nb
_ 0.2
Eq. (8)
For multiple turbines (i in number) the sum of impeller blade widths (Σwi) should be used for w and the average impeller ΣCi should be used for C in the equations which include these terms. np remains unchanged at the number of height i blades per turbine. With turbines having different diameters on the same shaft, a weighted average diameter based upon the exponents of D in the appropriate equation should be used. Propellers (baffled or unbaffled) For jackets: h jT k
æ D2 N ρ ö ÷ = 0.33 ç ç µ ÷ è ø
2/3
æ Cp µ ö ç ÷ ç k ÷ è ø
1/ 3
æ µ ç çµ è w
ö ÷ ÷ ø
0.14
æ µ ç çµ è w
ö ÷ ÷ ø
0.14
æDö ç ÷ èTø
−0.25
æCö ç ÷ èZø
0.15
æCö ç ÷ èZø
0.15
Eq. (9)
For helical coils: æ D2 N ρ ö hc T ÷ = 1.31 ç ç µ ÷ k è ø
0.56
æ Cp µ ö ç ÷ ç k ÷ è ø
1/ 3
æDö ç ÷ èTø
−0.25
Eq. (10)
Close Proximity Impellers
The following correlations apply to installations without wall scrapers. If scrapers are used, the values given by the equations should be multiplied by a factor of 1.3. Anchors: For NRe < 200 h jT k
æ D2 N ρ ö ÷ = 1.50 ç ç µ ÷ è ø
0.5
æ D2 N ρ ö ÷ = 0.36 ç ç µ ÷ è ø
2/3
æ Cp µ ö ç ÷ ç k ÷ è ø
1/ 3
æ µ ç çµ è w
ö ÷ ÷ ø
0.14
Eq. (11)
For NRe > 200 h jT k
æ Cp µ ö ç ÷ ç k ÷ è ø
1/ 3
æ µ ç çµ è w
ö ÷ ÷ ø
0.14
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Eq. (12)
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MIXING OPERATIONS
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HEAT TRANSFER IN AGITATED VESSELS DESIGN PRACTICES
December, 2001
HEAT TRANSFER CORRELATIONS AND DESIGN PROCEDURE (Cont) Helical Ribbons:
For 1 < NRe < 1000 h jT k
æ D2 N ρ ö ÷ = 4 .2 ç ç µ ÷ è ø
1/ 3
æ Cp µ ö ç ÷ ç k ÷ è ø
1/ 3
æ µ ç çµ è w
ö ÷ ÷ ø
0.2
Eq. (13)
For NRe > 1000 h jT k
æ D2 N ρ ö ÷ = 0.42 ç ç µ ÷ è ø
2/3
æ Cp µ ö ç ÷ ç k ÷ è ø
1/ 3
æ µ ç çµ è w
ö ÷ ÷ ø
0.14
Eq. (14)
When concentric banks of helical coils are used, the heat transfer coefficient, hc, for the coil bank closest to the impeller is as given by Eq. (4), (5), (7), or (10). For the second bank, hc, is 70% of the calculated value. For a third bank, if any, hc is 40% of the calculated value.
SERVICE SIDE HEAT TRANSFER COEFFICIENT For heating with condensing steam, a value for the service side coefficient, hs, of 1000 Btu/hr ft2 °F (5680 W/m2 °C) can be used. For cooling or heating with liquid the following correlations should be used. Note that flow channel equivalent diameter, de, is specifically defined for each jacket type. It is for heat transfer calculations only (not for pressure drop). The physical properties used are those of service fluid. Conventional Jacket (No Internal Baffles) hs de k
æ Cpµ ö ÷ 0.03 Re3 / 4 çç ÷ è k ø = éæ Cpµ ö ù ÷ − 1ú 1 + 1.74 Re−1/ 8 êçç ÷ êëè k ø úû
Eq. (15)
where: hs de s
= = =
Heat transfer coefficient, service fluid to vessel wall, Btu/hr ft2 °F (W/m2 °C) Equivalent flow channel diameter = 1.63s, ft (m) Jacket width, ft (m) (see Figure 2)
Re
=
Jacket Reynolds number = de (v i v A ) 0.5 + vB ρ / µ, dimensionless
vi
=
Nominal nozzle exit velocity
Qj di
= =
Volumetric flowrate of service fluid, ft3/hr (m3/s) Nozzle diameter, ft (m)
vA
=
Characteristic jacket velocity, radial fluid inlet =
[
]
Qi
π di2 / 4
, ft/hr (m/s)
Qj
π
(T22
tangential fluid inlet = T1, T2 L vB
β g
∆t
= = = = = =
− T12 ) / 4 Qj
sL / 2
, ft/hr (m/s)
, ft/hr (m/s)
Diameter to the inner and outer walls of the jacket, respectively, ft (m) Jacket length, ft (m) (see Figure 1) velocity due to natural convection = 0.5 (2 L β g ∆t)0.5, ft/hr (m/s) coefficient of cubical expansion of service liquid, °F-1 (°C-1) acceleration of gravity, ft/hr2 (m/s2) service fluid temperature change, °F (°C)
The addition of jacket baffles will enhance heat transfer, but no reliable correlations are available.
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HEAT TRANSFER CORRELATIONS AND DESIGN PROCEDURE (Cont) Half-Pipe Jacket
hs de = 0.023 k where: de dsi v
æ de v ρ ö çç ÷÷ è µ ø
= = =
0.8
æ Cp µ ö ç ÷ ç k ÷ è ø
1/ 3
æ µ ç çµ è w
ö ÷ ÷ ø
0.14
Eq. (16)
Equivalent pipe diameter = 1.57 dsi, ft (m) Jacket pipe internal diameter, ft (m) (Figure 3) Mean velocity in jacket, ft/hr (m/s)
Dimple Jacket
hs de = 0.052 k where: de
æ de v ρ ö çç ÷÷ è µ ø
=
0. 8
æ Cp µ ö ç ÷ ç k ÷ è ø
1/ 3
æ µ ç çµ è w
ö ÷ ÷ ø
0.14
Eq. (17)
Equivalent diameter = 0.055 ft (16.8 mm) for dimples on 2.5 in. (63.5 mm) square pitch
Helical Coils
hs dei = 0.023 k where: dci hs v
= = =
æ d ö æd vρö ç1 + 3.5 ci ÷ ç ci ÷ ç ÷ ç µ ÷ D c ø è ø è
0.8
æ Cρ µ ö ç ÷ ç k ÷ è ø
0. 4
Eq. (18)
Inside diameter of coil tube, ft (m) Heat transfer coefficient, service fluid to inside coil wall, Btu/hr ft2 °F (W/m2 °C) Service fluid velocity in coil, ft/hr (m/s)
SERVICE SIDE PRESSURE DROPS If the service side pressure drop is of concern, the pressure drop in simple coil arrangements can be estimated by the methods of Design Practices Section XIV. For pressure drops in jackets and complex coils, the specific equipment vendor or Reactor & Fluid Dynamics Section of EE should be consulted.
CALCULATION OF HEAT TRANSFER RATE The quantity of heat transferred through the jacket or coil heat transfer area is given by: q = U A ∆t m where: q A
= =
∆t m = U
=
Eq. (19) Rate of heat transfer, Btu/hr (W) Process side heat transfer area, ft2 (m2) Eq. (1) for jackets and Eq. (2) for helical coils] Log mean temperature between process and service fluids, °F (°C) Overall heat transfer coefficient, Btu/hr ft2 °F (W/m2 °C)
é A A Aδ 1 1 ù + + + + U= ê ú A h A h A k h h s fs m w p fp úû ëê s s where: As
=
Am =
δ
= 1/hf =
hp kw
= =
−1
Service side heat transfer area, ft2 (m2) A − As , ft2 (m2) Log mean transfer area = æ A ö ç ÷ In ç ÷ è As ø Wall thickness, ft (m) Fouling resistance (subscript p for process side, s for service side), [Btu/hr ft2 °F]-1 [W/m2 °C]-1 Process side heat transfer coefficient = hj or hc, Btu/hr ft2 °F (W/m2 °C) Wall thermal conductivity, Btu/hr ft2 °F/ft (W/m2 °C)
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Eq. (20)
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HEAT TRANSFER CORRELATIONS AND DESIGN PROCEDURE (Cont) Values for the fouling resistance, 1/hf, are tabulated for conventional heat exchangers in Section IX-B. Unless specific values are available, these resistances can also be used as an approximation in agitated vessels.
NON-NEWTONIAN FLUIDS The correlations for heat transfer coefficients given above were derived from studies with Newtonian fluids. With generally acceptable accuracy, the same correlations can be used for non-Newtonian fluids when the process fluid viscosity, µ, is replaced by the apparent viscosity, µA. For non-Newtonian fluids having power law behavior, the average shear rate, γA, to use in evaluating the viscosity is proportional to the rotational speed, N, of the impeller. Specifically for turbines and propellers:
γA = 10 N
Eq. (21)
Specific data on the fluid involved is required to calculate the apparent viscosity at this shear rate. Heat transfer coefficient correlations are also available for specific agitators in non-Newtonian fluids. Wilkinson reference or Reactor and Fluid Dynamics Section of EE should be consulted for their use.
The Edwards and
SAMPLE PROBLEM (The quantities in metric system are not exact, but rounded up.) Problem: Calculation of Cooling Coil Design for Agitated Reactor Given: A continuous flow reactor is 3 ft (0.9 m) in diameter and has a liquid depth of 3 ft (0.9 m). It is agitated by a 1 ft (0.3 m) diameter flat blade (6 blades) disk turbine (w/D = 1/5) operating at 350 rpm (5.83 rps). The turbine is located 1 ft (0.3 m) above the bottom of the tank and the reactor is equipped with baffles. The reaction being carried out releases 80,000 Btu/hr (23,500 W). It is desired to maintain the reactor contents at 120°F (49°C) by removing the reactor heat release and the agitator energy dissipation through the use of an internal cooling coil. The reactants enter at 120°F (49°C). All metal surfaces are stainless steel. Cooling water is available at 88°F (31°C). The physical properties of the liquid in the reactor are: Cp
=
0.8 Btu/lb °F
3350 J/kg °C
k
=
0.3 Btu/hr ft2 °F/ft
0.5 W/m °C
µ
=
4 lb/ft hr
1.6 x 10-3 Pa•s
ρ
=
60 lb/ft3
960 kg/m3
Cp (Cooling Water) = 1 Btu/lb °F Find: Design of internal cooling coil Solution: 1. Turbine energy dissipation [ Eq. (11) ], Section XIII-A
4180 J/kg °C
P = 2.62 x 10 −10 Np ρ N3 D5
P = N p ρ N 3 D 5 / 1000
= (2.62 x 10-10) (5) (60) (350)3 (1)5 = 3.37 HP
= (5)(960)(5.83)3 (0.3)5 / (1000) = 2.3 kW
or 2554
Btu / hr (3.37 hp) = 8600 Btu/hr hp
thus total heat to be removed = 80,000 + 8600 = 88,600 Btu/hr 2.
23,500 + 2,300 = 25,800 W
(Note that agitation contributes 10% of the heat to be removed) Heat transfer coefficient, process fluid to coil wall, [Eq. (7)] ækö hc = ç ÷ 2.68 èTø
hc =
0.56
æ D2 N ρ ö ç ÷ ç µ ÷ è ø
1/ 3
æ Cp µ ö ç ÷ ç k ÷ è ø
é (1)2 (350 x 60 ) (60) ù 0 .3 (2.68 ) ê ú 3 4 ëê ûú
hc = 530 Btu/hr ft2 °F
æ µ ç çµ è w
0.56
ö ÷ ÷ ø
0.14
æDö ç ÷ èTø 1/ 3
é ( 0 .8 ) ( 4 ) ù ê 0 .3 ú ë û
−0.3
æwö ç ÷ èTø 0.14
æ4ö ç ÷ è4ø
0.3
0.15
æCö np0.2 ç ÷ èZø
æ 1ö ç ÷ è3ø
−0.3
æ 0 .2 ö ç ÷ è 3 ø
æZö ç ÷ èTø 0.3
−0.5
(sin θ)0.5
æ 1ö (6)0.2 ç ÷ è3ø
hc = 3000 W/m2 °C
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0.15
æ3ö ç ÷ è3ø
−0.5
(sin 90 )0.5
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SAMPLE PROBLEM (Cont) 3.
Service fluid (cooling water) flow rate [assume 10°F (6°C) approach temperature]. Flowrate =
88,600 Btu/hr
=
(1Btu/lb °F) (110 − 88 °F) (62.0 lb/ft 3 )
25,800 ( 4180 ) ( 43 − 31) (1000 )
= 5.1 x 10 −4 m3 /s
= 65.0 ft 3 /hr if trial coil velocity of 10 ft/sec (3 m/s) is chosen, coil internal diameter is: 1/ 2
é 4 65.0 ft 3 /hr ù dci = ê ú êë π 36,000 ft/hr úû
1/ 2
é 4 5.1 x 10 − 4 ù dci = ê ú 3 êë π úû
= 0.0479 ft or 0.575 in.
= 0.0147 m
pick actual tubing as 3/4 in. (19 mm) o.d. x 0.083 in. (2.11 mm) wall (i.d. of 0.584 in. or 14.8 mm) and coil helix diameter of 0.75 T; therefore:
4.
dc
=
0.0625 ft
=
0.019 m
Dc
=
2.25 ft
=
0.675 m
dci
=
0.0487 ft
=
0.0147 m
v
=
9.69 ft/sec
=
2.95 m/s
Heat transfer coefficient, service fluid to inside coil wall [Eq. (18)] [for water, Cp = 1.0 Btu/lb°F (4180 J/kg°C), k = 0.35 Btu/hr ft2°F/ft (0.653 W/m°C), µ = 1.6 lb/ft hr (0.65 x 10-3 Pa•s), ρ = 62 lb/ft3 (994 kg/m3)]. k hs = (0.023 ) dci hs =
æ d ö æd vρö ç 1 + 3.5 ci ÷ ç ci ÷ ç ÷ ç µ ÷ D c ø è ø è
0.35 (0.023 ) 0.0487
0.8
æ Cp µ ö ç ÷ ç k ÷ è ø
é æ 0.0487 öù é (0.0487 ) (34,900 ) (62) ù ÷ú ê ê1 + 3.5 ç ú 1 .6 û è 2.25 øû ë ë
hs = 2340 Btu/hr ft2°F 5.
0.4
0.8
é (1) (1.6 ) ù x ê ú ë 0.35 û
0.4
hs = 13,300 W/m2°C
Overall heat transfer coefficient [Eq. (20)] (using fouling resistance 1/hf of 0.001(0.18 x 10-3 m2 °C/W) for both process and service sides, for stainless steel tubes kw = 8.55 Btu/hr ft2°F/ft (14.8 W/m°C), δ = 0.083 ft (0.00211 m). é A A Aδ 1 1 ù U=ê + + + + ú A s hfs Am k w hp hfp úû êë A s hs
−1
Using A/As = o.d./i.d. of coil tube and A/Am = o.d./mean diameter of the coil tube, U = 177 Btu/hr ft2°F 6.
U = 1005 W/m2°C
Required heat transfer area [Eq. (19)] A=
q = U ∆tm
88,600 = 26.5 ft 2 é ù ê ú 32 − 10 ú (177 ) ê ê æ 32 ö ú ê ln ç ÷ ú ë è 10 ø û
A=
25,800 = 2.35 m2 é 18 − 6 ù 1005 ê ú ë ln (18 / 6 ) û
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Section XIII-F
10 of 16
HEAT TRANSFER IN AGITATED VESSELS DESIGN PRACTICES
December, 2001
SAMPLE PROBLEM (Cont) 7.
Number of coil turns required [Eq. (2)] (assume Sc = dc) nt =
nt =
nt =
8.
A
[
π dc (π Dc ) + (Sc + dc ) 2 2
]
1/ 2
26.5
[
( π) (0.0625 ) { ( π) (2.25) } 2 + (0.0625 + 0.0625 )2
[
2.35
( π) (0.019) { ( π) (0.675 ) }2 + (0.019 + 0.019)2
]
]
1/ 2
1/ 2
= 19.1
= 18.6
therefore specify 19 helical turns, coil will have height Zc of 2.25 ft (0.7 m). Summary of cooling coil design dc
=
0.0625 ft or 0.75 in.
=
0.019 m
dci
=
0.0487 ft or 0.584 in.
=
0.0147 m
Hc
=
0.375 ft
=
0.114 m
Dc
=
2.25 ft
=
0.675 m
nt
=
19 turns
=
19 turns
Sc
=
0.0625 ft or 0.75 in.
=
0.019 m
Zc
=
2.25 ft
=
0.7 m
Tank baffles should be located inside of the coil helix.
NOMENCLATURE A As Am b B Bc C
= = = = = = =
Area of heat transfer surface (process side), ft2 (m2) Area of heat transfer surface (service side), ft2 (m2) Log mean transfer area, ft2 (m2) Distance between jacket baffles, ft (m) Baffle width, ft (m) Baffle clearance to vessel wall, ft (m) Impeller elevation above bottom of vessel, ft (m)
Cp dc dci de di dsi dso D Dc g
= = = = = = = = = =
Fluid heat capacity, Btu/lb°F (J/kg°C) Outside diameter of tube in coil, ft (m) Inside diameter of tube in coil, ft (m) Equivalent diameter, ft (m) Nozzle diameter, ft (m) Jacket pipe internal diameter, ft (m) Jacket pipe outside diameter, ft (m) Impeller diameter, ft (m) Diameter of coil helix, ft (m) Acceleration of gravity, ft/hr2 (m/s2)
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Section XIII-F
Page 11 of 16
December, 2001
NOMENCLATURE (Cont) hc
=
Heat transfer coefficient, vessel fluid to coil wall, Btu/(hr•ft2•°F) (W/m2°C)
hf
=
Fouling coefficient, Btu/(hr•ft2•°F) (W/m2°C)
hj
=
Heat transfer coefficient, vessel fluid to jacket wall, Btu/(hr•ft2•°F/ft) (W/m2°C)
hp
=
Heat transfer coefficient, process fluid side Btu/(hr•ft2•°F) (W/m2°C)
hs Hc i
= = =
Heat transfer coefficient, service fluid side, Btu/(hr• ft2•°F) (W/m2°C) Distance from bottom of vessel to lower end of coil bank, ft (m) Number of impellers
k
=
Fluid thermal conductivity, Btu/(hr•ft2•°F/ft) (W/m°C)
kw
=
Wall thermal conductivity, Btu/(hr•ft2•°F/ft) (W/m°C)
L np nt N Nb Np q Qj
= = = = = = = =
Vessel straight side, ft (m) Number of blades on turbine impeller Number of helical turns Impeller rotational speed, rpm (rps) Number of baffles Power number, dimensionless Rate of heat transfer, Btu/hr (W) Volumetric flowrate of service fluid, ft3/hr (m3/s)
Re
=
Jacket Reynolds number = de (v i v A ) 0.5 + v B
s Sc T T1,T2
= = = =
Jacket width, ft (m) Open space between coil turns, ft (m) Vessel diameter, ft (m) Overall diameter to the inner and outer wall of jacket, respectively, ft (m)
[
] ρµ , dim ensionless
∆t
=
Service fluid temperature change, °F (°C)
∆t m
=
Log mean temperature difference between process and service fluids, °F (°C)
U v vA vB vi w Z Zc
= = = = = = = =
Overall heat transfer coefficient, Btu/hr ft2°F (W/m2°C) Service fluid velocity in half-pipe jacket or cooling coil, ft/hr (m/s) Characteristic jacket velocity, ft/hr (m/s) Jacket velocity due to natural convection, ft/hr (m/s) Nozzle exit velocity, ft/hr (m/s) Blade width of impeller in direction parallel to axis of rotation, ft (m) Fluid depth in vessel, ft (m) Overall height of coil bank, ft (m)
β
=
Coefficient of cubical expansion, °F-1 (°C-1)
γA
=
Average shear rate, hr-1 (s-1)
δ
=
Heat transfer wall thickness, ft (m)
θ
=
Turbine blade angle from horizontal, degrees
µ
=
Fluid viscosity, lb/(ft•hr) (kg/ms or Pa•s)
µA
=
Apparent fluid viscosity, lb/(ft•hr) (kg/ms)
µw
=
Fluid viscosity at wall temperature, lb/ft•hr) (kg/ms)
ρ
=
Fluid density, lb/ft3 (kg/m3)
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MIXING OPERATIONS
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HEAT TRANSFER IN AGITATED VESSELS DESIGN PRACTICES
December, 2001
FIGURE 1 CONVENTIONAL JACKET
BC B
L Z w D
C
T
RELATIVE DIMENSIONS FOR A TYPICAL VESSEL B = T/12 to T/10 BC = B/6 C D w Z
= = = =
Z/3 T/3 D/8 to D/5 T DP13Ff01
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HEAT TRANSFER IN AGITATED VESSELS DESIGN PRACTICES
Section XIII-F
Page 13 of 16
December, 2001
FIGURE 2 CONVENTIONAL BAFFLED JACKET
b
S
DP13Ff02
FIGURE 3 HALF-PIPE JACKET
dsi
L
dso
DP13ff03
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MIXING OPERATIONS
HEAT TRANSFER IN AGITATED VESSELS DESIGN PRACTICES
December, 2001
FIGURE 4 DIMPLE JACKET
Dimples Welded to Vessel Wall
DP13Ff04
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HEAT TRANSFER IN AGITATED VESSELS DESIGN PRACTICES
Page 15 of 16
December, 2001
FIGURE 5 TYPICAL HELICAL COIL CONFIGURATION
T
dC dC i SC
ZC Z
w D HC DC
RELATIVE DIMENSIONS FOR TYPICAL HELICAL COILS
DC SC HC ZC
= 0.75 T ≥ dC = 0.15 T = 0.65 Z
DP13Ff05
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MIXING OPERATIONS
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HEAT TRANSFER IN AGITATED VESSELS DESIGN PRACTICES
December, 2001
FIGURE 6 TYPICAL BAFFLE COIL
BC
B
SC dC
Z
D C
T
RELATIVE DIMENSIONS FOR TYPICAL BAFFLE COIL
dC SC BC B
= = = =
0.02 T 0.03 T 0.02 T 0.2 T
DP13Ff06
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