Tinker's Flow Model for Shell & Tube Heat Exchanger Design

 TINKER’S FLOW MODEL FOR SHELL & TUBE HEAT EXCHANGER DESIGN

All the latest methods (Bell’s method) and many computer programs (HTRI, BJEC, Aspen EDR) for the process design of the heat exchangers without phase change are based on Tinker’s flow model.

If there is no phase change of shell side fluid then shell side heat transfer coefficient and the shell side pressure drop in all latest methods are calculated based on Tinker’s flow model. In conventional method for heat exchanger design like those developed by the Kern, it is assumed that entire shell side fluid is flowing across the tube bundle and between the baffles. But in really shell side fluid is flowing in various ways. In Tinker’s flow model the sell side flow is divided in total five different streams.

1.      Stream A

2.      Stream B

3.      Stream C

4.      Stream E

5.      Stream F

Fig 1: Tinker’s Flow Model

 

·        Stream A

Stream A is the tube-to-baffle leakage stream or it is the fraction of shell side fluid flowing through the clearance between tube hole in baffle and tube outside diameter. This stream does not bypass the heat transfer area (outside area of tubes) and hence, it does not create any adverse effect on the value of heat transfer coefficient. However, it makes the significant difference in pressure drop (loss). When stream A leaves this clearance, it forms free flowing jet. Hence, boundary layer separation occurs and considerable friction loss or pressure drop takes place. Effect of stream A must be considered in the calculation of pressure drop.

 

·        Stream B

Stream B is the actual cross flow stream or it is the fraction of shell side fluid which is flowing across the tube bundle and between the baffles. In Kern’s method and other old methods, it is assumed that entire shell side fluid is flowing like stream B.

 

·        Stream C

Stream C is bundle to shell bypass stream or it is the fraction of shell side fluid flowing through the clearance area between shell inside diameter and tube bundle. Stream C is the main bypass stream. (bypassing the heat transfer area). This clearance area provides low pressure drop path for the shell side fluid. Hence, % of shell side fluid bypassed through this clearance area is quite significant. It is maximum with pull through floating head heat exchanger and minimum with fixed tube sheet heat exchanger. Amount of stream C can be reduced considerably by using sealing strips which are attached on inside surface of shell. They provide the partial blockage or the additional resistance in the path of stream C.

 

·        Stream E

Stream E is the baffle to shell leakage stream. It is a part of shell side fluid flowing through the clearance between the edge of baffle and shell wall. Like stream C, this stream is also bypassing the heat transfer area and hence, reduces shell side heat transfer coefficient. But amount of stream E is lesser than amount of stream C. Normally, the clearance between baffle outside diameter and shell inside diameter is in the range of 1.6 to 4.8 mm while clearance between tube bundle and shell inside diameter is in the range of 10 to 100 mm.

 

 

·        Stream F

Stream F is the pass-partition bypass stream. In tube sheets where pass partition plates are attached (for forming tube side passes), in that portion tubes cannot be provided. In multipass heat exchangers, one can find more number of gaps in tube bundle. Stream F is the fraction of shell side fluid flowing through these gaps. If the gap is vertical it provides low pressure drop path for fluid flow. Just like stream C and stream E, this stream is also bypassing the heat transfer area and reduces shell side heat transfer coefficient. Amount of stream F and its adverse effects are significant in multipass heat exchanger. To reduce the amount of this stream sometimes dummy tubes are used.

 

NOTE: There is no stream designated as stream “D”.

 

SELECTION CRITERIA BETWEEN HORIZONTAL  CONDENSER AND VERTICAL CONDENSER 

• Selection of the orientation of the condenser plays important role in the design. If someone selects wrong orientation then condenser will not give the desired performance.

Some selection criteria between horizontal condenser and vertical condenser are described as below:

1.  Only for the case of     filmwise condensation, horizontal position givers higher     condensation coefficient than vertical position. In filmwise condensation, the thickness of     condensate film on the heat transfer surface governs the value of the condensation coefficient. With horizontal position and shell side condensation, the condensate travels less distance over the heat transfer surface before detaching from the heat transfer surface and falling down by gravity compared to the vertical position. With vertical position, condensate travels over the entire tube length before falling down by the effect of gravity. 

Hence average condensate film thickness in the case of horizontal position is less than that of obtained in the case of vertical position and hence, it can provide higher condensation coefficient.

2.  In case of condensation with     subcooling in a shell & tube heat exchanger, condensation coefficient is higher for horizontal position but the subcooling coefficient is higher for vertical position.

In case of subcooling with horizontal position, small fraction of gravitational force is acting on the pool of condensate and hence, condensate is flowing with almost no turbulence (Laminar flow). Hence, subcooling with horizontal position is natural convection heat transfer. While in subcooling with vertical position, entire gravitational force is acting on pool of condensate. Hence, it creates turbulence in pool of condensate and provides higher subcooling coefficient (Turbulent flow). Subcooling with vertical position can be considered as forced convection heat transfer. 

 

Therefore, in case of condensation with subcooling, shell and tube heat exchanger is design for both position (Vertical and Horizontal) and the position which gives higher value of the overall heat transfer coefficient is selected.

3.  In case of condensation with non-condensable, selection of position depends on the percentage of non-condensable present in inlet vapour. For which guidelines are given by Frank.

(a) If non-condensable are < 0.5% (by mass), then the presence of noncondensables is ignored in design calculations. Heat exchanger is designed as a     total condenser. For this case, horizontal position should be selected as it provides the higher condensation coefficient.

 

(b) If non-condensable are > 70% (by mass), then for the entire flow rate, without phase change correlation is applied to calculate the heat transfer coefficient. However, in calculation of heat duty (ft), condensation is considered. For this case, selection of the position does not depend on heat transfer coefficient, as without phase change coefficient does not depend on position of heat exchanger so in this case position is decided by other factors like available area or available height.

 

(c) Between 0.5 to 70% non-condensable, heat transfer coefficient is determined by considering both condensation as well as cooling of non-condensable and vapours. For this case horizontal position should be selected as it gives higher condensation coefficient, if condensation with cooling is carried out on shell side. If the same is carried out on tube side, then vertical position is better, because dry gas film over the heat transfer surface is continuously swept away by incoming stream.

Types of Reboiler for Distillation Column

 

TYPES OF REBOILER FOR DISTILLATION COLUMN

●  REQUIREMENT OF REBOILER FOR DISTILLATION COLUMN

As we all know that distillation column is used to separate component from mixture. Distillation column is used to contact vapor and liquid due to that mass transfer occurs. Liquid is coming from tray above to tray below and vapor is going to tray above to tray below. Generally, vapor is generated by vaporizing bottom liquid.

Required heat in reboiler is provided by the high-pressure steam or heat transfer oils or some hot fluid available in the plant. For the liquid having high boiling point, generally fuel-fired furnace is used.

·         DIFFERENT TYPES OF REBOILERS USED WITH DISTILLATION COLUMN

Different types of reboilers are used to generate vapours in distillation column are described below:

1.      Jacketed Kettle Reboiler:

      Small Fractionating columns used for the pilot plant; these types of jacketed kettle type reboiler are used. Vapor generated by jacketed kettle is very low.

Construction: Jacket is provided around the distillation column sump to provide sufficient heat to the liquid. Steam or heat transfer oil is supplied in the jacket to provide heat to the liquid. Refer Fig 1.

 

 

 

Fig. 1: Jacketed Kettle Reboiler

 

 

2.      Internal Reboiler:

Internal reboiler provides large heat transfer area compared to the jacket kettle reboiler. We can use floating head type rear head for the tube bundle which will take care of thermal expansion of tubes. But when scaling occurs on the outer surface of the tubes, we need to remove entire tube bundle from the column for the maintenance purpose. Vapour issuing column from jacket kettle and internal reboiler is equilibrium with the residue product. We can consider one stage of distillation column so the required stage will decrease by one. Sometimes these types of reboilers are known as bundle in column reboiler.

Construction: Tube bundle is constructed in the column itself. Inside the tube heating medium is supplied to provide heat to the liquid. Refer Fig 2.

 

 

 

 

Fig. 2: Internal Reboiler

 

3.      Kettle Type Reboiler:

Like jacket kettle and internal reboiler, vapor generated in kettle type reboiler is always in equilibrium with residue product so e can consider kettle type reboiler as one stage.

Construction: this type of reboiler receives liquid from column by gravity and heating medium is circulated inside the tubes. Vapor generated in reboiler is fed back to the column. Liquid coming out from the overflow wear is taken out as residue product. This type of reboiler is generally used with the vacuum distillation column because it provides low pressure drop. Refer Fig 3.

 

 

 

Fig. 3: Kettle Type Reboiler

 

 

4.      Thermosyphon Reboiler:

Vapor generated in this reboiler has the same composition as the liquid entering the reboiler. It is safe to not to consider the thermosyphon reboiler as one stage, instead of that it is safe to provide extra stage in the distillation column itself.

Construction: In vertical thermosyphon reboiler heating medium is fed in shell side and the liquid which is to be vaporised is fed inside the tubes. Refer Fig 4.

 

 

Fig. 4: Vertical Thermosyphon Reboiler

  

External reboilers are used with large distillation columns with the spares for cleaning and maintenance purpose. 

JOULE’S EXPERIMENT || INTERNAL ENERGY || FIRST LAW OF THERMODYNAMICS

●  JOULE’S EXPERIMENT

Today’s concept of heat developed by the crucial experiments carried out in the 1840s by James P. Joule.

At that time Joule has performed multiple experiments with water, oil and mercury.  In that experiments he took known amounts of water, oil or mercury in an isolated vessel and agitated the fluid with stirrer.

He noted the power given to fluid by the rotating stirrer. He noticed that the temperature of the fluid was increased. He precisely measured the amount of work done on the fluid by the stirrer (Power input to the Stirrer) and the resulting temperature changes in the fluid (T_final – T_intial).

He showed that for each type fluid certain amount of work per unit mass of fluid was required to raise the temperature by 1 degree by stirring. And the previous temperature of fluid is restored by the simple heat transfer with cooler object.

These experiments demonstrated the existence of a quantitative relationship between work and heat, and thereby showed that heat is a form of energy.

 ●  INTERNAL ENERGY:

In experiments like those performed by the James P. Joule, Energy added to the fluid as a work by the agitator and transferred to the cooler object is later known as the “HEAT”.

A general question is: Where does the energy stored after its addition to the fluid and before its transfer from the fluid?

Answer to this question is that it is contained within the fluid in another form of energy which is known as “INTERNAL ENERGY”.

Internal energy of a substance does not count energy that is may possess as a result of the gross movement or position as a whole. It refers to energy of the molecules comprising the substance. Due to ceaseless motion all molecules comprising the substance possess the kinetic energy of translation.

The addition of heat to a substance increases molecular motion and thus causes an increase in the internal energy of the substance. Work done on the substance also have the same effect as shown by James P. Joule. Potential energy associated with the intermolecular forces are also counted as internal energy. Energy is associated with the interactions of electrons and nuclei of atoms on a sub-molecular scale, which includes the energy of chemical bonds that hold atoms together as molecules.

Name internal energy distinguishes from external forms the potential, static or kinetic energy associated with a substance because of its macroscopic motion, position or configuration which are considered as external forms of energy.

There is no precise thermodynamic definition of internal energy. Measurement of internal energy of any thermodynamic system cannot be measured. There is no instrument available to measure internal energy. Absolute value of internal value are unknown. This is not disadvantage in thermodynamic analysis because the absolute value of internal energy of system is not required only changes in internal energy are required.

●  THE FIRST LAW OF THERMODYNAMICS

The first law of thermodynamics is also known as principle of conservation of mechanical energy. It also includes heat and internal energy in addition to work and external potential and kinetic energy. In generally, it can be extended to other forms of energy like surface energy, electrical energy and magnetic energy.

“Although energy assumes many forms, the total quantity of energy is constant, and when energy disappears in one form it appears simultaneously in other forms.”

To apply this law to a particular process, the process is divided into two parts, the system and its surrounding. Region in which process occurs is known as system and everything outside the system is known as surroundings. System and surrounding is separated by boundary, boundary may be rigid or flexible, real or imaginary. The first law of thermodynamics applies to system and its surroundings; not to the system alone. For thermodynamic process, the first law requires:

∆ (Energy of the system) + ∆ (Energy of the surroundings) = 0

(Note: ∆ is Difference Operator)

In thermodynamic language, heat and work represent energy in transit across the boundary dividing the system from its surroundings, and never stored in system nor contained in the system. On the other hand, potential, kinetic and internal energy stored with matter. Heat and Work represents energy flows from or to a system.

The sum of change in energy of system and change in energy of surrounding is zero. This is known as first law of thermodynamics.

 

INTRODUCTION TO SHELL & TUBE HEAT EXCHANGER

First question comes in our mind by hearing this word is that what is heat exchanger?

Answer to this question is that, heat exchanger is a mechanical device that transfer heat from one fluid to another fluid. It utilizes the principle of conduction and convection.

There are three steps in heat transfer in heat exchanger.

  STEP 1 : Heat is transferred from the hot fluid to the inner wall of tube by the means of  convective heat transfer.

   STEP 2 :  Heat is transferred from inner wall of the tube to outer wall of tube by the means of conduction.

   STEP 3 : Heat is transferred from outer wall of tube to the cold fluid by the means of convection.

 

There are many types of heat exchangers are available in chemical industries for the heating or cooling application but among all of that shell & tube heat exchanger are most widely used in chemical process industries.

Shell & Tube heat exchangers are mainly used as heat transfer equipment but in few cases shell & tube heat exchanger is also used as the reactor & falling film absorber. Sizing of various parts of shell & tube heat exchanger like tubes, shell, baffles, pass partition plate & tie rods are standardized. These standards are developed by TEMA (Tubular Exchanger Manufacturers Association) USA and HTRI (Heat Transfer Research Institute) USA. IS:4503 is also equivalent to TEMA and used for the process design of the shell & tube heat exchanger and it also specify the maximum allowable baffle spacing, minimum tube sheet thickness, baffle thickness, numbers of tie rods required, etc.

For mechanical design and fabrication of shell & tube heat exchanger ASME (American Society of Mechanical Engineers) Section VIII div II is used along with IS:2825.

Shell & Tube heat exchanger are divided in three types according to TEMA standard:

1. Class R covers heat exchangers which are used for severe duties in petroleum and related industries. Also, it covers heat exchangers that are going to handle toxic gas, highly flammable fluid or hazardous fluid.

2. Class B covers the heat exchangers which are used in chemical process industries not involving severe duties.

3. Class C covers the heat exchangers which are used in commercial and in less important process applications. Example: Heat exchangers used for recovery of energy from an effluent stream.

Process Design of Shell & Tube Heat Exchanger:

One can easily do the process design of shell & tube heat exchanger manually with the help of books, some books are listed below:

1.  Perry, R. H., and D. Green, Perry’s Chemical Engineers’ Handbook, 6th Ed., McGraw-Hill, USA, 1984.

2.  Sinnott, R. K., Coulson and Richardson’s Chemical Engineering, Vol. 6, Revised 2nd Ed., Asian Publishers Books Pvt. Ltd., New Delhi, 1998.

3.  Kern, D. Q., Process Heat Transfer, McGraw-Hill, USA, 1950.

4.  Ludwig, E. E, Applied Process Design for Chemical and Petrochemical Plants, Vol.3, 3rd Ed. Gulf   Publishing, USA, 2001.

Apart from books listed above there are many more books are available for process design of shell & tube heat exchanger. We can also perform the design calculation of shell & tube heat exchanger in the software.

Most popular and reliable softwares used for the design of shell and tube heat exchangers are as follows:

1.      HTRI: Heat Transfer Research Inc., USA

2.      HTFS: Heat Transfer and Fluid Flow Services, UK

3.      BJAC: USA based company

4.      HEI: Heat Exchange Institute, USA.

5.      Aspen EDR (Exchanger Design & Rating): A software by the Aspen Technology.

Design methods and equations that are used by these softwares are proprietary and are not available in open literature. For the design of shell and tube heat exchanger involving fluid without phase change, methods used by these softwares are based on Tinker’s flow model.

Energry Balance For Closed System

 

ENERGY BALANCE FOR CLOSED SYSTEM

"If the matter does not transfer from boundary to surrounding or from surrounding to system then this type of system is known as closed system and mass of closed system should be constant, However energy can cross the boundary." One can easily develop basic concepts in thermodynamics by carefully observing system.

Most of industrial processes are open system, in which matter crosses the system boundary as streams that enter and leave process equipment.

No streams enter or leave the closed system, no energy associated with the matter is transported across the boundary that divides the system from surroundings. All energy transfer between a closed system and surroundings is in the form of heat or work. Total energy change of the surroundings equals the net energy transferred to or from it as heat and work only.

∆ (Energy of the system) + ∆ (Energy of the surroundings) = 0..........Eq (1)

Second term of equation may be replaced by variables which represents as heat and work, to get.

∆ (Energy of surroundings) = ± Q ± W..........Eq (2)

Where Q is heat and W is work to the system. And the sign for numerical value depends in which direction heat and work is flowing with respect to the system or surroundings.

If we adopt the convention that makes the numerical values of both quantities positive for transfer into the system from surroundings. The corresponding quantities taken with reference to the surroundings, Q_surr and W_surr , have the opposite sign. Q_surr = -Q and W_surr = -W.

∆ (Energy of surroundings) = Q_surr + W_surr = - Q - W..........Eq (3)

With this logic equation 1 becomes:

∆ (Energy of system) = Q + W Eq..........(4)

Equation 4 indicates that the total energy change of a closed system equals the net energy transferred into it as heat and work.

In closed system often undergo processes in which change in external energy is zero only the internal energy of the system changes. Foe this type of processes equation 4 becomes:

∆ U^t = Q +W Eq..........(5)

Where U^t is the total internal energy of the system. For differential changes in U^t :

dU^t = dQ+ dW  Eq..........(6)

In equation 3, equation 4, equation 5 and equation 6 all terms require to be expressed is same energy units. For SI system unit of the energy is joule (J). For British system unit of energy is (British Thermal Unit).

For closed system containing n numbers of moles, equation 5 and equation 6 becomes

∆ (nU) = n(∆U) = Q +W  Eq..........(7)

d(nU) = n(dU) = dQ +dW  Eq..........(8)

In this form, these equations show explicitly the amount of substance comprising the system.

These equations of thermodynamics are many times written for a certain unit amount of material, either a unit mole or unit mass. For n=1 equation 7 and equation 8 becomes:

∆ U = Q +W and dU = dQ + dW

Above equations do not provide a definition of internal energy. Indeed, they presume prior affirmation of the existence of internal energy, as expressed in the following axiom:

Axiom 1: There exists a form of energy, known as internal energy U, which is an intrinsic property of a system, functionally related to the measurable coordinates that characterize the system. For a closed system, not in motion, changes in this property are given by Eq. (7) & (8).

Equations 7 and 8 not only helps to calculate changes in internal energy from experimental measurements, but they also helps us to derive the property relations that connects directly to measurable quantities like temperature and pressure. These two equation have dual purpose, because once internal energy values are known, they provide for the calculation of heat and work quantities for practical processes. By accepting the above axiom and associated definition of a system and surroundings, one can state the first law of thermodynamics as a second axiom:

Axiom 2: (The First Law of Thermodynamics) The total energy of any system and its surroundings is conserved.

Van Der Waas Equation of State (EOS)

         What is Equation of State (EOS) ?

• Equation of state is thermodynamic expression which relates the pressure (P), temperature (T) and the volume (V).

The perfect gas equation fails to explain the PVT behavior of real gases as the volume occupied by the molecules of a real gas and the forces of interaction between them are not negligible as in ideal gas.

Van Der Waals equation takes into account these two features of a real gas by incorporate certain correction factors in the pressure and volume terms of the ideal gas equation.

Van Der Waals proposed following equation to explain the PVT Behavior of the Real Gases :

Where a and b are van der waals constants.

This equation is cubic in volume and it gives three real roots below the critical temperature.

•         Largest root indicates vapor volume
•        Smallest root indicates liquid volume
•        Intermediate root has no significance

 

At saturation pressure, smallest and the largest roots represents the molar volumes of saturated liquid and saturated vapour respectively.
 
Constants are evaluated by following equations : 

Where Tc and Pc are critical temperature and pressure respectively.

We can the difference in results obtained by the ideal gas law and van der waals equation of state from following problem

Problem Statement :

1 kmol of CO₂ occupies a volume 0.381 m³ at 313 K. Compare the pressures given by the ideal gas law and van der waals equation of state.

Take Van Der Waals constant

                          a = 0.365  Nm⁴/mol²

                               b = 4.28 * 10^-5  m³/mol

Solution :

Date Given :

Molar Volume (V) = 0.381 * 10^-3 m³/mol

Temperature (T) = 313 K

Gas Constant (R) = 8.314 Nm/mol.K

By Ideal Gas Law :

 

By Van Der Waals EOS :

From the above results we can see that result obtained from the ideal gas law is different than that is obtained from the van der waals equation of state and ideal gas equation cannot be applicable on the real gases.