Heat Exchangers: Design, Operation, Maintenance and Enhancement

Ali A. Rabah (BSc., MSc., PhD., MSES) Department of chemical engineering, University of Khartoum, P.O. Box 321, Khartoum, Sudan

Email: [email protected]

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Table of contents

Table of contents 1 Introduction 8 1.1 Programm outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.2 Instructor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2 Classification of heat exchangers 2.1 Classification by construction . . . . . . . . . . . . . . . . . . . . 2.1.1 Tubular heat exchanger . . . . . . . . . . . . . . . . . . . 2.2 Double pipe heat exchanger . . . . . . . . . . . . . . . . . . . . . 2.3 Spiral tube heat exchanger . . . . . . . . . . . . . . . . . . . . . . 2.4 Shell and tube heat exchanger . . . . . . . . . . . . . . . . . . . . 2.4.1 Fixed tubesheet . . . . . . . . . . . . . . . . . . . . . . . . 2.4.2 U-tube . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.3 Floating head . . . . . . . . . . . . . . . . . . . . . . . . . 2.5 Plate heat exchangers . . . . . . . . . . . . . . . . . . . . . . . . 2.5.1 Gasketed plate heat exchanger . . . . . . . . . . . . . . . 2.5.2 Welded- and Brazed-Plate exchanger (W. PHE and BHE) 2.5.3 Spiral Plate Exchanger (SPHE) . . . . . . . . . . . . . . . 2.6 Extended surface . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6.1 Plate fin . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6.2 Tube fin . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Code and standards 3.1 TEMA Designations . . . . . . . . . 3.2 Classification by construction STHE 3.2.1 Fixed tube sheet . . . . . . . 3.2.2 U-Tube Heat Exchanger . . . 3.2.3 Floating Head Designs . . . . 3.3 Shell Constructions . . . . . . . . . . 3.4 Tube side construction . . . . . . . . 3.4.1 Tube-Side Header: . . . . . . 3.4.2 Tube-Side Passes . . . . . . . 3.4.3 Tubes Type . . . . . . . . . . 3.4.4 Tube arrangement . . . . . . 3.4.5 Tube side passes . . . . . . . 3.5 Shell side construction . . . . . . . . 3.5.1 Shell Sizes . . . . . . . . . . . 3.5.2 Shell-Side Arrangements . . . 3.6 Baffles and tube bundles . . . . . . . 3.6.1 The tube bundle . . . . . . .

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Dr. Ali A. Rabah, Dept of Chemeng, U of K, Email : [email protected]

Table of contents

3.6.2 3.6.3 3.6.4 3.6.5 3.6.6

Baffle . . . . . . . . . . Vapor Distribution . . . Tube-Bundle Bypassing Tie Rods and Spacers . . Tubesheets . . . . . . .

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4 Basic Design Equations of Heat Exchangers 4.1 LMTD-Method . . . . . . . . . . . . . . . . . . 4.1.1 Logarithmic mean temperature different 4.1.2 Correction Factor . . . . . . . . . . . . . 4.1.3 Overall heat transfer coefficient . . . . . 4.1.4 Heat transfer coefficient . . . . . . . . . 4.1.5 Fouling factor (hid , hod ) . . . . . . . . . . 4.2 ε- NTU . . . . . . . . . . . . . . . . . . . . . . 4.3 Link between LMTD and NTU . . . . . . . . . 4.4 The Theta Method . . . . . . . . . . . . . . . .

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5 Thermal Design 5.1 Design Consideration . . . . . . . . . . . . . . . . 5.1.1 Fluid Stream Allocations . . . . . . . . . . 5.1.2 Shell and tube velocity . . . . . . . . . . . 5.1.3 Stream temperature . . . . . . . . . . . . 5.1.4 Pressure drop . . . . . . . . . . . . . . . . 5.1.5 Fluid physical properties . . . . . . . . . . 5.2 Design data . . . . . . . . . . . . . . . . . . . . . 5.3 Tubeside design . . . . . . . . . . . . . . . . . . . 5.3.1 Heat-transfer coefficient . . . . . . . . . . 5.3.2 Pressure drop . . . . . . . . . . . . . . . . 5.4 Shell side design . . . . . . . . . . . . . . . . . . . 5.4.1 Shell configuration . . . . . . . . . . . . . 5.4.2 Tube layout patterns . . . . . . . . . . . . 5.4.3 Tube pitch . . . . . . . . . . . . . . . . . . 5.4.4 Baffling . . . . . . . . . . . . . . . . . . . 5.4.5 Equalize cross-flow and window velocities . 5.4.6 Shellside stream analysis (Flow pattern) . 5.4.7 Heat transfer coefficient and pressure drop 5.4.8 Heat transfer coefficient . . . . . . . . . . 5.4.9 Pressure drop . . . . . . . . . . . . . . . . 5.5 Design Algorithm . . . . . . . . . . . . . . . . . . 6 Specification sheet

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Dr. Ali A. Rabah, Dept of Chemeng, U of K, Email : [email protected]

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Table of contents

6.1 6.2 6.3 6.4

Information included . . . . Information not included . . Operation conditions . . . . Bid evaluation . . . . . . . . 6.4.1 Factor to be consider

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7 Storage, Installation, Operation and Maintenance 7.1 Storage . . . . . . . . . . . . . . . . . . . . . . . . . 7.2 Installation . . . . . . . . . . . . . . . . . . . . . . 7.2.1 Installation Planning . . . . . . . . . . . . . 7.2.2 Installation at Jobsite . . . . . . . . . . . . 7.3 Operation . . . . . . . . . . . . . . . . . . . . . . .

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8 Heat exchanger tube side mainenance (Repair vs replacement 8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2 Repair vs. Replace - Factors To Consider . . . . . . . . . . . . . . 8.3 Heat Exchanger maintenance Options . . . . . . . . . . . . . . . . 8.4 Repair option . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.4.1 Plug . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.4.2 Sleeving . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.4.3 Tube Expansion . . . . . . . . . . . . . . . . . . . . . . . . 8.5 Replacement option . . . . . . . . . . . . . . . . . . . . . . . . . . 8.5.1 Retubing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.5.2 Rebundling . . . . . . . . . . . . . . . . . . . . . . . . . . 8.5.3 Complete replacement (New unit) . . . . . . . . . . . . . . 8.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Troubleshooting 9.1 Heat exchangers’ problems . . . . . . . . . . . 9.2 Fouling . . . . . . . . . . . . . . . . . . . . . . 9.2.1 Costs of fouling . . . . . . . . . . . . . 9.2.2 Facts about fouling . . . . . . . . . . . 9.2.3 Types of Fouling . . . . . . . . . . . . 9.2.4 Fouling Mechanisms . . . . . . . . . . 9.2.5 Conditions Influencing Fouling . . . . . 9.2.6 Fouling control . . . . . . . . . . . . . 9.2.7 Fouling cleaning methods . . . . . . . 9.3 Leakage/Rupture of the Heat Transfer Surface 9.3.1 Cost of leakage . . . . . . . . . . . . . 9.3.2 Cause of differential thermal expansion 9.4 Corrosion . . . . . . . . . . . . . . . . . . . .

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Dr. Ali A. Rabah, Dept of Chemeng, U of K, Email : [email protected]

Table of contents

9.5 9.6

9.7 9.8

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9.4.1 Corrosion effects . . . . . . . . . . . . . . . . . . . 9.4.2 Causes of corrosion . . . . . . . . . . . . . . . . . . 9.4.3 Type of corrosion . . . . . . . . . . . . . . . . . . . 9.4.4 Stress corrosion . . . . . . . . . . . . . . . . . . . . 9.4.5 Galvanic corrosion . . . . . . . . . . . . . . . . . . 9.4.6 Pitting . . . . . . . . . . . . . . . . . . . . . . . . . 9.4.7 Uniform or rust corrosion . . . . . . . . . . . . . . 9.4.8 Crevice corrosion . . . . . . . . . . . . . . . . . . . 9.4.9 Materials of Construction . . . . . . . . . . . . . . 9.4.10 Fabrication . . . . . . . . . . . . . . . . . . . . . . Troubleshooting . . . . . . . . . . . . . . . . . . . . . . . . Past failure incidents . . . . . . . . . . . . . . . . . . . . . 9.6.1 Ethylene Oxide Redistillation Column Explosion: . 9.6.2 Brittle Fracture of a Heat Exchanger . . . . . . . . 9.6.3 Cold Box Explosion . . . . . . . . . . . . . . . . . . Failure scenarios and design solutions . . . . . . . . . . . . Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.8.1 Use of Potential Design Solutions Table . . . . . . . 9.8.2 Special Considerations . . . . . . . . . . . . . . . . Troubleshooting Examples . . . . . . . . . . . . . . . . . . 9.9.1 Shell side temperature uncontrolled . . . . . . . . . 9.9.2 Shell assumed banana-shape . . . . . . . . . . . . . 9.9.3 Steam condenser performing below design capacity 9.9.4 Steam heat exchanger flooded . . . . . . . . . . . .

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10 Unresolved problems in the heat exchangers design 120 10.1 Future trend . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 Bibliography A Heat transfer coefficient A.1 Single phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . A.1.1 Inside tube: Turbulent flow . . . . . . . . . . . . . . . A.1.2 Inside tube: Laminar flow . . . . . . . . . . . . . . . . A.1.3 Shell side . . . . . . . . . . . . . . . . . . . . . . . . . A.1.4 Plate heat exchanger . . . . . . . . . . . . . . . . . . . A.2 Condensation . . . . . . . . . . . . . . . . . . . . . . . . . . . A.2.1 Condensation on vertical plate or outside vertical tube A.2.2 Condensation on external horizontal tube . . . . . . . A.2.3 Condensation on banks of horizontal tube . . . . . . . A.2.4 Condensation inside horizontal tube . . . . . . . . . . .

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Dr. Ali A. Rabah, Dept of Chemeng, U of K, Email : [email protected]

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A.3 Two phase flow: Pure fluid . . . . . . . . . . . . A.3.1 Steiner [140] correlation . . . . . . . . . A.3.2 Kattan et al. [77] correlation . . . . . . . A.3.3 Kandlikar [70] correlation . . . . . . . . A.3.4 Chen [19] correlation . . . . . . . . . . . A.3.5 Gungor and Winterton [52] correlation . A.3.6 Shah [130] correlation . . . . . . . . . . . A.3.7 Schrock and Grossman [129] correlation . A.3.8 Dembi et al. [30] correlation . . . . . . . A.3.9 Klimenko [84] correlation . . . . . . . . . A.3.10 Jung et al. [64] correlation . . . . . . . . A.4 Two phase flow: Mixture . . . . . . . . . . . . . A.4.1 Steiner [140] correlation . . . . . . . . . A.4.2 Kandlikar [71] correlation . . . . . . . . A.4.3 Bennett and Chen [8] correlation . . . . A.4.4 Palen [111] correlation . . . . . . . . . . A.4.5 Jung et al. [64] correlation . . . . . . . . B Pressure drop B.1 Single phase . . . . . . . . . . . . . . . . . B.2 Two phase . . . . . . . . . . . . . . . . . . B.2.1 Friedel [42] model . . . . . . . . . B.2.2 Lockhart and Martinelli [91] model B.2.3 Chisholm [22] model . . . . . . . .

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C Physical properties C.1 Physical properties: Pure fluid . . . . . . . . . . . C.1.1 Specific heat . . . . . . . . . . . . . . . . . C.1.2 Vapor pressure . . . . . . . . . . . . . . . C.1.3 Liquid viscosity . . . . . . . . . . . . . . . C.1.4 Vapor dynamic viscosity VDI-W¨armeatlas C.1.5 Dynamic viscosity of Fenghour et al. [40] . C.1.6 Surface tension . . . . . . . . . . . . . . . C.1.7 Thermal conductivity for liquids . . . . . . C.1.8 Thermal conductivity for gases . . . . . . C.1.9 Specific enthalpy . . . . . . . . . . . . . . C.2 Physical properties: Mixture . . . . . . . . . . . . C.2.1 Liquid dynamic viscosity of mixtures . . . C.2.2 Vapor dynamic viscosity of mixtures . . . C.2.3 Liquid thermal conductivity of mixtures .

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Dr. Ali A. Rabah, Dept of Chemeng, U of K, Email : [email protected]

Table of contents

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C.2.4 Vapor thermal conductivity of mixtures . . . . . . . . . . . . . . . . 154 C.2.5 Surface tension of mixtures . . . . . . . . . . . . . . . . . . . . . . 155 C.3 Software packages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155

Dr. Ali A. Rabah, Dept of Chemeng, U of K, Email : [email protected]

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1 Introduction

1

Introduction

Heat exchanger is an important and expensive item of equipment that is used almost in every industry (oil and petrochemical, sugar, food, pharmaceutical and power industry). A better understanding of the basic principles of heat transfer and fluid flow and their application to the design and operation of heat exchangers that you gain from this course will enable you to improve their efficiency and extend their life. You understand how to use the applicable API, TEMA and ASME recommended practices, standards and codes for heat exchangers. This will enable you to communicate with the designers, manufacturers and bidders of heat exchangers. You will understand how to avoid fouling, corrosion and failure and leak problems by your design. You will also be able to survey and troubleshoot heat exchangers and assist in performing inspection, cleaning, and maintenance. You will be exposed to recent development and future trend in heat exchangers. The course includes worked examples to reinforce the key learning as well as a demonstration of mechanical design and challenging problems encountered in the operation of heat exchangers. Objectives • To learn the classification, code and standards (API, TEMA,...) and selection procedure for heat exchangers. • To review the thermal and mechanical design of heat exchangers. • To learn the installation, operation and maintenance procedure for heat exchanger. • To acquire information that will enable decisions to be made on the repair and refurbishment of aging equipment as well as repair vs. replacement options. • To learn techniques of failure elimination and appropriate maintenance and troubleshooting procedures. • To delineate the factors that lead to overall economically advantageous decisions. Who should attend: Project engineers, process engineers and plant engineers in the oil, chemical, sugar, power, and other industries who requires a wider and deeper appreciation of heat exchangers design, performance and operation. The detailed review of thermal and mechanical design is particularly useful to plant and maintenance engineers as well as to those generally knowledgeable in the subject, but who require a refresher or update. Codes and standards are useful for project engineer to help him communicate with manufacturers, designers and bidders of heat exchangers. Troubleshooting procedures are important for process engineers. Participants will be taken through an intensive primer of heat transfer principles as applicable to heat exchangers.

1.1

Programm outline

1. DAY I: HEAT EXCHANGERS CLASSIFICATION APPLICATION, CODE AND STANDARDS • • • • • •

Classification according to construction (tubular, plate, finned, enhanced) Classification according to service (cooler, heater, condenser, reboiler, etc..) Construction, applications, range and limitations and sizes Code and standards (TEMA, API,...) TEMA nomenclature: rear end head types, shell types, font end types TEMA standards: shell size, tube size, baffle, selection of materials, component design, nozzle loadings, supports, lifting features, high pressure, low temperature, specials designs

Dr. Ali A. Rabah, Dept of Chemeng, U of K, Email : [email protected]

1.1 Programm outline

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2. DAY II HEAT TRANSFER FUNDAMENTALS AND THERMAL DESIGN • Heat transfer mechanisms: conduction and convection as related to heat exchangers • Temperature difference in heat exchanger: – LMTD Method – ε-NTU Method – θ-Method • Overall heat transfer coefficient • Heat transfer coefficient and pressure drop for single phase and multiphase (evaporation and condensation) • Resistances to fouling • Illustration examples using the software CHEMCAD 3. DAY III MECHANICAL DESIGN OF HE • Mechanical design: shells, channels and heads, tubesheets, bundles, tubestubesheet attachment • Design strategy, design algorithm • Heat exchanger: – Selection procedure – Specification sheet – Bid evaluation • Worked example (USING CHEMCAD) 4. DAY IV Storage, Installation, Operation, Maintenance • • • • • • • •

Storage Installation procedure Operation start up shut down Maintenance Cleaning Repair – Plug – Sleeving – Expansion • Replacement – Retubing – Rebundling – Replacement (new unit)

5. DAY V Troubleshooting • Heat exchangers’ problem Dr. Ali A. Rabah, Dept of Chemeng, U of K, Email : [email protected]

10

1 Introduction

– Fouling: causes, mechanisms, design considerations and exchanger selection, remedies, cleaning – Leakage: Location (tube sheet, tube failure), causes (differential thermal expansion, flow-induced vibration), – Corrosion: Type, causes, material of construction, fabrication – Vibration: causes (velocity), design procedure to avoid vibration including baffle selection, rod baffles, impingement baffles • Past incidents failure. • Examples of common problems encountered in heat exchangers (low rate, uncontrolled outlet temperature, failure of tubes near the inlet nozzles) Achieve the learning outcomes to: Understand the principles of heat transfer and fluid flow, application of industry practices and a substantial amount of supporting data needed for design, performance and operation of modern heat exchangers. Gain insight not only into shell and tube heat exchangers but also heat transfer fundamentals as applied to heat exchangers, the types of heat exchangers and their application, and recent advance in heat exchanger technologies Become familiar with the practical aspects and receive tips on shell and tube heat exchanger thermal design and rating: mechanical design and rating using the applicable API, TEMA and ASME recommended practices, standards and codes, troubleshooting, and performance improvement and enhancement Avoid future problems by gaining insight into vibration forcing mechanisms Enhance your awareness of causes of failure and learn practical ways for determining and correcting them Daily Schedule: 8:00 Registration and Coffee (1st day only) 8:30 Session begins 4:30 Adjournment There will be a forty-minute lunch break each day in addition to refreshment and networking break of 20 minutes during each morning and afternoon session.

1.2

Instructor

Faculty: Ali. Rabah, BSc. MSc., PhD., MSES., Assistant professor, Department of Chemical Engineering University of Khartoum Dr. Rabah holds a BSc. degree (Chemical Engineering) from the University of Khartoum, MSc. degree from university of Nairobi, Kenya, and PhD. degree from University of Hannover, Germany. He has a wide professional experience in teaching heat and mass transfer and engineering thermodynamics to BSc and MSc Chemical, Mechanical and Petroleum Engineering students. Dr. Rabah is a consultant engineer to a number of chemical industries and factories. He has developed and delivered numerous designs of heat exchangers, evaporators and boilers. He designed, for example, a 5 ton/hr (10 bar) fired tube boiler. His design is under fabrication. Dr. Rabah has designed and manufactured double pipe heat exchangers for education proposes to a number of chemical engineering departments country-wide e.g. University of Nileen. Dr. Rabah assumed engineering design positions with responsibilities covering design, construction and inspection of heat transfer equipments. The design projects are sponsored by the federal ministry of research and technology and the University of Khartoum consultancy cooperation. Dr. Ali A. Rabah, Dept of Chemeng, U of K, Email : [email protected]

1.2 Instructor

11

Dr. Rabah is a member of the Sudan Engineering Society (SES) and serving as a member of editorial board of SES Journal. He is a reviewer to a number of world wide software packages for chemical engineering simulations and the prediction of thermodynamic properties. Dr. Rabah has a number of publications in field of heat transfer and thermodynamics.

Dr. Ali A. Rabah, Dept of Chemeng, U of K, Email : [email protected]

12

2

2 Classification of heat exchangers

Classification of heat exchangers

The word exchanger really applies to all types of equipment in which heat is exchanged but is often used specially to denote equipment in which heat is exchanged between two process streams. Exchangers in which a process fluid is heated or cooled by a plant service stream are referred to as heatsers and coolers. If the process stream is vaporized the exchanger is called a vaporizer if the the stream is essentially completely vaporized: called a reboiled if associated with a distillation column: and evaporator if used to concentrate a solution. If the process fluid is condensed the exchanger is called a condenser. The term fired exchanger is used for exchangers heated by combustion gases, such as boiler. In heat exchanger the heat transfer between the fluid takes place through a separating wall. The wall may a solid wall or interface. Heat exchangers are used in • Oil and petrochemical Industry (upstream and down stream) • Sugar industry • Power generation industry • Air-cooling and refrigeration industry These heat exchanger may be classified according to: • Transfer process 1. Direct contact 2. indirect contact (a) Direct transfer type (b) Storage type (c) Fluidized bed • Surface compactness 1. Compact (surface area density ≥ 700m2 /m3 ) 2. non-compact (surface area density < 700m2 /m3 ) • Construction 1. Tubular (a) Double pipe (b) Shell and tube (c) Spiral tube 2. Plate (a) Gasketed (b) Spiral plate (c) Welded plate 3. Extended surface (a) Plate fin (b) Tube fin 4. Regenerative (a) Rotory i. Disc-type Dr. Ali A. Rabah, Dept of Chemeng, U of K, Email : [email protected]

13

ii. Drum-type (b) Fixed-matrix • Flow arrangement 1. Single pass (a) Parallel flow (b) Counter flow (c) Cross flow 2. Multipass (a) Extended surface H.E. i. Cross counter flow ii. Cross parallel flow (b) Shell and tube H.E. i. Parallel counter flow (Shell and fluid mixed, M shell pass, N Tube pass) ii. Split flow iii. Divided flow (c) Plate H.E. (N-parallel plate multipass) • Number of fluids 1. Two-fluid 2. Three fluid 3. N-fluid (N > 3) • Transfer mechanisms 1. 2. 3. 4.

Single phase convection on both sides Single phase convection on one side, two-phase convection on the other side Two-phase convection on both sides Combined convection and radiative heat transfer

• Classification based on service: Basically, a service may be single phase (such as the cooling or heating of a liquid or gas) or two-phase (such as condensing or vaporizing). Since there are two sides to an STHE, this can lead to several combinations of services. Broadly, services can be classified as follows: single-phase (both shellside and tubeside); condensing (one side condensing and the other single-phase); vaporizing (one side vaporizing and the other side single-phase); and condensing/vaporizing (one side condensing and the other side vaporizing). The following nomenclature is usually used: – Heat exchanger: both sides singlephase and process streams (that is, not a utility). – Cooler: one stream a process fluid and the other cooling water or air. Dirty water can be used as the cooling medium. The top of the cooler is open to the atmosphere for access to tubes. These can be cleaned without shutting down the cooler by removing the distributors one at a time and scrubbing the tubes. – Heater: one stream a process fluid and the other a hot utility, such as steam or hot oil. – Condenser: one stream a condensing vapor and the other cooling water or air. Dr. Ali A. Rabah, Dept of Chemeng, U of K, Email : [email protected]

14

2 Classification of heat exchangers

– Chiller: one stream a process fluid being condensed at sub-atmospheric temperatures and the other a boiling refrigerant or process stream. By cooling the falling film to its freezing point, these exchangers convert a variety of chemicals to the solid phase. The most common application is the production of sized ice and paradichlorobenzene. Selective freezing is used for isolating isomers. By melting the solid material and refreezing in several stages, a higher degree of purity of product can be obtained. – Reboiler: one stream a bottoms stream from a distillation column and the other a hot utility (steam or hot oil) or a process stream. – Evaporators:These are used extensively for the concentration of ammonium nitrate, urea, and other chemicals sensitive to heat when minimum contact time is desirable. Air is sometimes introduced in the tubes to lower the partial pressure of liquids whose boiling points are high. These evaporators are built for pressure or vacuum and with top or bottom vapor removal. – Absorbers: These have a two-phase flow system. The absorbing medium is put in film flow during its fall downward on the tubes as it is cooled by a cooling medium outside the tubes. The film absorbs the gas which is introduced into the tubes. This operation can be cocurrent or countercurrent. – Falling-Film Exchangers: Falling-film shell-and-tube heat exchangers have been developed for a wide variety of services and are described by Sack [Chem. Eng. Prog., 63, 55 (July 1967)]. The fluid enters at the top of the vertical tubes. Distributors or slotted tubes put the liquid in film flow in the inside surface of the tubes, and the film adheres to the tube surface while falling to the bottom of the tubes. The film can be cooled, heated, evaporated, or frozen by means of the proper heat-transfer medium outside the tubes. Tube distributors have been developed for a wide range of applications. Fixed tube sheets, with or without expansion joints, and outside-packed-head designs are used. Principal advantages are high rate of heat transfer, no internal pressure drop, short time of contact (very important for heat-sensitive materials), easy accessibility to tubes for cleaning, and, in some cases, prevention of leakage from one side to another. These falling-film exchangers are used in various services as described in the following paragraphs. Among these classifications the classification by construction is the most widely used one.

2.1

Classification by construction

The principal types of heat exchanger are listed again as 1. Tubular exchanger 2. Plate exchanger 3. Extended surface 4. Regenerative 2.1.1 Tubular heat exchanger Tubular heat exchanger are generally built of circular tubes. Tubular heat exchanger is further classified into: • Double pipe heat exchanger • Spiral tube heat exchanger • Shell and tube heat exchanger Dr. Ali A. Rabah, Dept of Chemeng, U of K, Email : [email protected]

2.2 Double pipe heat exchanger

2.2

15

Double pipe heat exchanger

This is usually consists of concentric pipes. One fluid flow in the inner pipe and the other fluid flow in the annulus between pipes. The two fluid may flow concurrent (parallel) or in counter current flow configuration; hence the heat exchanger are classified as: • counter current double pipe heat exchanger (see Fig. 4.1and Fig. 2.2)and • cocurrent double pipe heat exchanger

Figure 2.1. Double pipe heat exchanger. Courtesy of Perry, Chemical engineering hand book Elbew 3/4"

Tee 2"x1/2"

Galv. pipe Threaded 3/4"

Galv. pipe 2"

Union 2" Part A Cu pipe 3/4"

Tee 3/4"x1/2"

Part B

Flanged Gland 2"

Specification Sheet

Valve 3/4"

Item

pump

Double Pipe Heat Exchanger Scale: None Sheet No.1 Date: 08.12.2003 Designed by: Dr.-Ing. Ali A. Rabah

Qty

Item

Qty

Tee 2"x3/4"

6

Tee 3/4"x1/2"

14

Union 2"

6

Cu Bush 1/2"

8

Valve 3/4"

4

Elbew 3/4"

10

Galv. pipe 2"x3ft 3

Cu pipe 3/4"x4ft

3

Galv. pipe 3/4"x1ft

Selector

(Threaded)

24

(20 Channel)

1

Cu Flange 2"

8

Flow meter 3/4"

2

Pump 0-40 l/min 2

Union 3/4"

30

Amplifier

Microvoltmeter

1

Elbew 1/2"

4

Union 1/2"

8

1

Thermocouples (NiCr-Ni)

10

Flow meter

Bypass

Bypass

Figure 2.2. Double pipe heat exchanger (Counter current)

Double pipe heat exchanger is perhaps the simplest of all heat exchanger types. The advantages of this type are: Dr. Ali A. Rabah, Dept of Chemeng, U of K, Email : [email protected]

16

2 Classification of heat exchangers

i Easily by disassembly, no cleaning problem ii Suitable for high pressure fluid, (the pressure containment in the small diameter pipe or tubing is a less costly method compared to a large diameter shell.) Limitation: The double pipe heat exchanger is generally used for the application where the total heat transfer surface area required is less than or equal to 20 m2 (215 ft2 ) because it is expensive on a cost per square meter (foot) basis.

2.3

Spiral tube heat exchanger

Spiral tube heat exchanger consists of one or more spirally wound coils fitted in a shell (Fig. 2.3). Heat transfer associated with spiral tube is higher than than that for a straight tube . In addition, considerable amount of surface area can be accommodated in a given space by spiralling. Thermal expansion is no problem but cleaning is almost impossible.

Figure 2.3. Spiral tube heat exchanger. Courtesy of The German Atlas

2.4

Shell and tube heat exchanger

Shell and tube heat exchanger is built of round tubes mounted in a cylindrical shell with the tube axis parallel to that of the shell. One fluid flow inside the tube, the other flow across and along the tubes. The major components of the shell and tube heat exchanger are tube bundle, shell, front end head, rear end head, baffles and tube sheets (Fig.2.4).

Figure 2.4. Shell and tube heat exchanger

Dr. Ali A. Rabah, Dept of Chemeng, U of K, Email : [email protected]

2.4 Shell and tube heat exchanger

17

The shell and tube heat exchanger is further divided into three catogaries as 1. Fixed tube sheet 2. U tube 3. Floating head 2.4.1 Fixed tubesheet A fixed-tubesheet heat exchanger (Figure 2.5) has straight tubes that are secured at both ends to tubesheets welded to the shell. The construction may have removable channel covers , bonnet-type channel covers , or integral tubesheets. The principal advantage of the fixedtubesheet construction is its low cost because of its simple construction. In fact, the fixed tubesheet is the least expensive construction type, as long as no expansion joint is required.

Figure 2.5. Fixed-tubesheet heat exchanger.

Other advantages are that the tubes can be cleaned mechanically after removal of the channel cover or bonnet, and that leakage of the shellside fluid is minimized since there are no flanged joints. A disadvantage of this design is that since the bundle is fixed to the shell and cannot be removed, the outsides of the tubes cannot be cleaned mechanically. Thus, its application is limited to clean services on the shellside. However, if a satisfactory chemical cleaning program can be employed, fixed-tubesheet construction may be selected for fouling services on the shellside. In the event of a large differential temperature between the tubes and the shell, the tubesheets will be unable to absorb the differential stress, thereby making it necessary to incorporate an expansion joint. This takes away the advantage of low cost to a significant extent. 2.4.2 U-tube As the name implies, the tubes of a U-tube heat exchanger (Figure 2.6) are bent in the shape of a U. There is only one tubesheet in a Utube heat exchanger. However, the lower cost for the single tubesheet is offset by the additional costs incurred for the bending of the tubes and the somewhat larger shell diameter (due to the minimum U-bend radius), making the cost of a U-tube heat exchanger comparable to that of a fixedtubesheet exchanger. Dr. Ali A. Rabah, Dept of Chemeng, U of K, Email : [email protected]

18

2 Classification of heat exchangers

The advantage of a U-tube heat exchanger is that because one end is free, the bundle can expand or contract in response to stress differentials. In addition, the outsides of the tubes can be cleaned, as the tube bundle can be removed. The disadvantage of the U-tube construction is that the insides of the tubes cannot be cleaned effectively, since the U-bends would require flexible- end drill shafts for cleaning. Thus, U-tube heat exchangers should not be used for services with a dirty fluid inside tubes.

Figure 2.6. U-tube heat exchanger.

2.4.3 Floating head The floating-head heat exchanger is the most versatile type of STHE, and also the costliest. In this design, one tubesheet is fixed relative to the shell, and the other is free to ”float” within the shell. This permits free expansion of the tube bundle, as well as cleaning of both the insides and outsides of the tubes. Thus, floating-head SHTEs can be used for services where both the shellside and the tubeside fluids are dirty-making this the standard construction type used in dirty services, such as in petroleum refineries. There are various types of floating- head construction. The two most common are the pull-through with backing device and pullthrough without backing service designs. The design (Figure 2.7) with backing service is the most common configuration in the chemical process industries (CPI). The floating-head cover is secured against the floating tubesheet by bolting it to an ingenious split backing ring. This floating-head closure is located beyond the end of the shell and contained by a shell cover of a larger diameter. To dismantle the heat exchanger, the shell cover is removed first, then the split backing ring, and then the floating-head cover, after which the tube bundle can be removed from the stationary end. Dr. Ali A. Rabah, Dept of Chemeng, U of K, Email : [email protected]

2.5 Plate heat exchangers

19

Figure 2.7. Floating head with packing service.

In the design without packing service construction (Figure 2.8), the entire tube bundle, including the floating-head assembly, can be removed from the stationary end, since the shell diameter is larger than the floating-head flange. The floatinghead cover is bolted directly to the floating tubesheet so that a split backing ring is not required. The advantage of this construction is that the tube bundle may be removed from the shell without removing either the shell or the floatinghead cover, thus reducing maintenance time. This design is particularly suited to kettle reboilers having a dirty heating medium where Utubes cannot be employed. Due to the enlarged shell, this construction has the highest cost of all exchanger types.

Figure 2.8. Floating head without packing service.

2.5

Plate heat exchangers

These exchangers are generally built of thin plates. The plate are either smooth or have some form of corrugations and they are either flat or wound in exchanger. Generally Dr. Ali A. Rabah, Dept of Chemeng, U of K, Email : [email protected]

20

2 Classification of heat exchangers

theses exchanger cannot accomodate high pressure/temperature differential relative the tubular exchanger. This type of exchanger is further classified as: • Gasketed plate • Fixed plate • Spiral plate 2.5.1 Gasketed plate heat exchanger Gasketed plate heat exchanger (see Fig. 2.9) consists of a series of corrugated alloy material channel plates, bounded by elastomeric gaskets are hung off and guided by longitudinal carrying bars, then compressed by large-diameter tightening bolts between two pressure retaining frame plates (cover plates).

Figure 2.9. Plate heat exchanger

The frame and channel plates have portholes which allow the process fluids to enter alternating flow passages (the space between two adjacent-channel plates) Fig.2.10. Gaskets around the periphery of the channel plate prevent leakage to the atmosphere and also prevent process fluids from coming in contact with the frame plates. No inter fluid leakage is possible in the port area due to a dual-gasket seal. Fig.2.11 shows the plate profiles. Expansion of the initial unit is easily performed in the field without special considerations. The original frame length typically has an additional capacity of 15-20 percent more channel plates (i.e. surface area). In fact, if a known future capacity is available during fabrication stages, a longer carrying bar could be installed, and later, increasing the surface area would be easily handled. When the expansion is needed, simply untighten the carrying bolts, pull back the frame plate, add the additional channel plates, and tighten the frame plate. Dr. Ali A. Rabah, Dept of Chemeng, U of K, Email : [email protected]

2.5 Plate heat exchangers

21

Figure 2.10. Plate heat exchanger flow configuration

Applications: Most PHE applications are liquid-liquid services but there are numerous steam heater and evaporator uses from their heritage in the food industry. Industrial users typically have chevron style channel plates while some food applications are washboard style. Fine particulate slurries in concentrations up to 70 percent by weight are possible with standard channel spacings. Wide-gap units are used with larger particle sizes. Typical particle size should not exceed 75 percent of the single plate (not total channel) gap. Close temperature approaches and tight temperature control possible with PHE’s and the ability to sanitize the entire heat transfer surface easily were a major benefit in the food and pharmaceutical industry. Advantages: • Easily assembled and dismantled • Easily cleaned both chemically and mechanically • Flexible (the heat transfer can be changed as required) • Can be used for multiple service as required • Leak is immediately deteced since all plates are vented to the atmosphere, and the fluid split on the floor rather than mixing with other fluid • Heat transfer coefficient is larger and hence small heat transfer area is required than STHE • The space required is less than that for STHE for the same duty • Less fouling due to high turbulent flow Dr. Ali A. Rabah, Dept of Chemeng, U of K, Email : [email protected]

22

2 Classification of heat exchangers

Figure 2.11. Plate and frame of a plate heat exchanger

• Very close temperature approach can be obtained • low hold up volume • LMTD is fully utilized • More economical when material cost are high Disadvantages: • Low pressure Mc Cpc ⇒ Cmin = Mc Cpc , Cmax = Mh Cph

(4.19)

Qmax = Cmin (Thi − Tci )

(4.20)

Cmin Cmax

(4.21)

Thi − Tho Tco − Tci , εc = Thi − Tci Thi − Tci

(4.22)

∆Tc Tspan

(4.23)

C=

εh =

ε=

where Tspan is defined in fig. 4.5 for counter current flow Dr. Ali A. Rabah, Dept of Chemeng, U of K, Email : [email protected]

4.2 ε- NTU

63

Thi

Tco Tho

Tspan

∆θ Tci 0

A

Figure 4.5. Temperature distribution in counter current flow

The ε equation for various heat exchanger configuration is given as • Parallel flow

1 − exp [−N (1 + C)] 1+C

(4.24)

1 − exp [−N (1 + C)] 1 − C exp [−N (1 − C)]

(4.25)

ε= • Counter current flow ε= • Cross flow 1. Both fluid unmixed mixed

"

exp(−N Cn) − 1 ε = 1 − exp Cn where

#

(4.26)

n = N −0.22

(4.27)

2. Both fluid mixed "

C 1 1 + − ε= 1 − exp(−N ) − 1 1 − exp(−N C) − 1 N

#−1

(4.28)

3. Cmax mixed, Cmin unmixed ε=

1 {1 − exp [−C (1 − exp(−N ))]} C

(4.29)

Dr. Ali A. Rabah, Dept of Chemeng, U of K, Email : [email protected]

64

4 Basic Design Equations of Heat Exchangers

4. Cmax unmixed, Cmin mixed ½

¾

ε = 1 − exp −

1 [1 − exp(−N C)] C

(4.30)

• One shell pass, 2,4, 6 tube passes   

q

(1 + C 2 )

ε=2 1+C +  

• Condenser • Evaporator

h

q

i

h

q

i

−1  1 + exp −N (1 + C 2 ) 

 1 − exp −N (1 + C 2 ) 

(4.31)

ε = 1 − e−N

(4.32)

ε = 1 − e−N

(4.33)

Alternatively these equations are presented in a graphical form. The various curves of ε vs N T U can be found in textbooks like Kern (1964( and Perry and Green (2000).

4.3

Link between LMTD and NTU

• Cocurrent

µ

∆T1 ∆T2

¶

∆T1 ln ∆T2

¶

ln • Counter current

4.4

µ

µ

Thi − Tci Tho − Tco

¶

Thi − Tco = ln Tho − Tci

¶

= ln µ

= N h + Nc

(4.34)

= Nh − Nc

(4.35)

The Theta Method

Alternative method of representing the performance of heat exchangers may be given by Theta method [146] as Θ=

∆Tm Tspan

(4.36)

where ∆Tm is the mean temperature difference and Tspan is the maximum temperature difference (Thi −Tci ) (see Fig. 4.5). The Theta method is related is related to the associated ε and N T U methods by expressions Θ=

ε ∆Tm = Tspan NT U

(4.37)

The relationship between parameters are often presented in graphical form as shown in Fig.4.6. However, they all depend on finding ∆Tm or ∆Tlm

Dr. Ali A. Rabah, Dept of Chemeng, U of K, Email : [email protected]

4.4 The Theta Method

65

Figure 4.6. θ correction charts for mean temperature difference: (a) One shell pass and any multiple of two tube passes. (b) Two shell passes and any multiple of four tube passes.[121].

Dr. Ali A. Rabah, Dept of Chemeng, U of K, Email : [email protected]

66

5 Thermal Design

5

Thermal Design

5.1

Design Consideration

5.1.1 Fluid Stream Allocations There are a number of practical guidelines which can lead to the optimum design of a given heat exchanger. Remembering that the primary duty is to perform its thermal duty with the lowest cost yet provide excellent in service reliability, the selection of fluid stream allocations should be of primary concern to the designer. There are many trade-offs in fluid allocation in heat transfer coefficients, available pressure drop, fouling tendencies and operating pressure. • The higher pressure fluid normally flows through the tube side. With their small diameter and nominal wall thicknesses, they are easily able to accept high pressures and avoids more expensive, larger diameter components to be designed for high pressure. If it is necessary to put the higher pressure stream in the shell, it should be placed in a smaller diameter and longer shell. • Place corrosive fluids in the tubes, other items being equal. Corrosion is resisted by using special alloys and it is much less expensive than using special alloy shell materials. Other tube side materials can be clad with corrosion resistant materials or epoxy coated. • Flow the higher fouling fluids through the tubes. Tubes are easier to clean using common mechanical methods. • Because of the wide variety of designs and configurations available for the shell circuits, such as tube pitch, baffle use and spacing, multiple nozzles, it is best to place fluids requiring low pressure drops in the shell circuit. • The fluid with the lower heat transfer coefficient normally goes in the shell circuit. This allows the use of low-fin tubing to offset the low transfer rate by providing increased available surface. Quiz: The top product of a distillation column is condensed using sea water. Allocate the fluids in the tube and the shell of the heat exchanger?. 5.1.2 Shell and tube velocity High velocities will give high heat transfer coefficients but also a high pressure drop and cause erosion. The velocity must be high enough to prevent any suspended solids settling, but not so high as to cause corrosion. High velocities will reduce fouling. Plastic inserts are sometimes used to reduce erosion at the tube inlet. Typical design velocity are given below:

Liquids 1. Tube-side process fluids:1 to 2 m/s, maximum 4 m/s if required to reduce fouling: water 1.5 to 2.5 m/s 2. Shell side: 0.3 to 1/m/s Dr. Ali A. Rabah, Dept of Chemeng, U of K, Email : [email protected]

5.1 Design Consideration

67

Vapors For vapors, the velocity used will depend on the operating pressure and fluid density; the lower values in the range given below will apply to molecular weight materials Vacuum 50 to 70 m/s Atmospheric pressure 10 to 30 m/s High pressure 5 to 10 m/s 5.1.3 Stream temperature The closer the temperature approach used (the difference between the outlet temperature of one stream and the inlet temperature of the other stream) the larger will be the heat transfer area required for a given duty. The optimum value will depend on the application and can only be determined by making an economic analysis of alternative designs. As a general guide the greater temperature difference should be at least 20 o C. and the least temperature difference 5 to 7 o C for cooler using cooling water and 3 to 5 o C using refrigerated brine. The maximum temperature rise in recirculated cooling water is limited to around 30 o C. Care should be taken to ensure that cooling media temperatures are kept well above the freezing point of the process materials. When heat exchange is between process fluids for heat recovery the optimum approach temperatures will normally not be lower than 20 o C. 5.1.4 Pressure drop The value suggested below can be used as a general guide and will normally give designs that are near the optimum.

Liquids Viscosity 1,000), the heattransfer coefficient varies to the 0.6-0.7 power of velocity; however, pressure drop varies Dr. Ali A. Rabah, Dept of Chemeng, U of K, Email : [email protected]

5.4 Shell side design

75

to the 1.7-2.0 power. For laminar flow (Re < 100), the exponents are 0.33 for the heattransfer coefficient and 1.0 for pressure drop. Thus, as baffle spacing is reduced, pressure drop increases at a much faster rate than does the heat-transfer coefficient. This means that there will be an optimum ratio of baffle spacing to shell inside diameter that will result in the highest efficiency of conversion of pressure drop to heat transfer. This optimum ratio is normally between 0.3 and 0.6. Baffle cut. As shown in Figure 5.3, baffle cut is the height of the segment that is cut in each baffle to permit the shellside fluid to flow across the baffle. This is expressed as a percentage of the shell inside diameter. Although this, too, is an important parameter for STHE design, its effect is less profound than that of baffle spacing.

Figure 5.3. Baffle cut.

Baffle cut can vary between 15% and 45% of the shell inside diameter. Both very small and very large baffle cuts are detrimental to efficient heat transfer on the shellside due to large deviation from an ideal situation, as illustrated in Figure 5.4.

Figure 5.4. Effect of small and large baffle cuts.

It is strongly recommended that only baffle cuts between 20% and 35% be employed. Reducing baffle cut below 20% to increase the shellside heat-transfer coefficient or increasing the baffle cut beyond 35% to decrease the shellside pressure drop usually lead to poor designs. Other aspects of tube bundle geometry should be changed instead to achieve those goals. For example, doublesegmental baffles or a divided-flow shell, or even a cross-flow shell, may be used to reduce the shellside pressure drop. Dr. Ali A. Rabah, Dept of Chemeng, U of K, Email : [email protected]

76

5 Thermal Design

For single-phase fluids on the shellside, a horizontal baffle cut (Figure 5.5) is recommended, because this minimizes accumulation of deposits at the bottom of the shell and also prevents stratification. However, in the case of a two-pass shell (TEMA F), a vertical cut is preferred for ease of fabrication and bundle assembly.

Figure 5.5. Baffle cut orientation

5.4.5 Equalize cross-flow and window velocities Flow across tubes is referred to as cross-flow, whereas flow through the window area (that is, through the baffle cut area) is referred to as window flow. The window velocity and the cross-flow velocity should be as close as possible - preferably within 20% of each other. If they differ by more than that, repeated acceleration and deceleration take place along the length of the tube bundle, resulting in inefficient conversion of pressure drop to heat transfer. 5.4.6 Shellside stream analysis (Flow pattern) On the shellside, there is not just one stream, but a main cross-flow stream and four leakage or bypass streams, as illustrated in Figure 5.6. Tinker (4) proposed calling these streams the main cross-flow stream (B), a tube-to-baffle-hole leakage stream (A), a bundle bypass stream (C), a pass-partition bypass stream (F), and a baffle-to-shell leakage stream (E). While the B (main cross-flow) stream is highly effective for heat transfer, the other streams are not as effective. The A stream is fairly efficient, because the shellside fluid is in contact with the tubes. Similarly, the C stream is in contact with the peripheral tubes around the bundle, and the F stream is in contact with the tubes along the passpartition lanes. Consequently, these streams also experience heat transfer, although at a lower efficiency than the B stream. However, since the E stream flows along the shell wall, where there are no tubes, it encounters no heat transfer at all. The fractions of the total flow represented by these five streams can be determined for a particular set of exchanger geometry and shellside flow conditions by any sophisticated heatexchanger thermal design software. Essentially, the five streams are in parallel and flow along paths of varying hydraulic resistances. Thus, the flow fractions will be such that the pressure drop of each stream is identical, since all the streams begin and end at the inlet and outlet nozzles. Subsequently, based upon the efficiency of each of these streams, the overall shellside stream efficiency and thus the shellside heat-transfer coefficient is established. Dr. Ali A. Rabah, Dept of Chemeng, U of K, Email : [email protected]

5.4 Shell side design

77

Figure 5.6. Tube arrangement

Since the flow fractions depend strongly upon the path resistances, varying any of the following construction parameters will affect stream analysis and thereby the shellside performance of an exchanger: • baffle spacing and baffle cut; • tube layout angle and tube pitch; • number of lanes in the flow direction and lane width; • clearance between the tube and the baffle hole; • clearance between the shell I.D. and the baffle; and • location of sealing strips and sealing rods. Using a very low baffle spacing tends to increase the leakage and bypass streams. This is because all five shellside streams are in parallel and, therefore, have the same pressure drop. The leakage path dimensions are fixed. Consequently, when baffle spacing is decreased, the resistance of the main cross-flow path and thereby its pressure drop increases. Since the pressure drops of all five streams must be equal, the leakage and bypass streams increase until the pressure drops of all the streams balance out. The net result is a rise in the pressure drop without a corresponding increase in the heat-transfer coefficient. The shellside fluid viscosity also affects stream analysis profoundly. In addition to influencing the shellside heat transfer and pressure drop performance, the stream analysis also affects the mean temperature difference (MTD) of the exchanger. This will be discussed in detail later. First, though, let’s look at an example that demonstrates how to optimize baffle design when there is no significant temperature profile distortion. 5.4.7 Heat transfer coefficient and pressure drop For the shell side heat transfer coefficient and pressure drop there are a number of methods these include: • Kern’s method • Donohue’s method • Bell-Delaware method • Tinker’s method Dr. Ali A. Rabah, Dept of Chemeng, U of K, Email : [email protected]

78

5 Thermal Design

Besides these methods there is some proprietary methods putout by various organization for use by their member companies. A number of these method are based on one of the above methods. Some are based upon a judicious combination of methods 3 and 4 above and supplemented by further research data. Among the most popular of the proprietary methods, judged by their large clientele are • Heat Transfer Research Inc. (HTRI), Alliambra, california. This method is also known as stream analysis method. • Heat Transfer and Fluid Flow Service (HTFS), Engineering Science Division, AERE, Harwell, United Kingdom Method. In this work only Kern’s method is given below. Bell-Delaware method may be found in Coulson and Richardson’s 5.4.8

Heat transfer coefficient Ã

N u = 0.36Re where

Nu = Pr = Re = de = A= P = G= As = pt = Ds = lB =

hde k Cp µ k Gde µ 4A P

M As (pt −do )Ds lB pt

0.55

Pr

1/3

µ µw

!0.14

,

(5.7)

Nusselt number Prandtl number Reynolds number hydraulic diameter cross-sectional flow area wetted perimeter Mass flux fluid viscosity at the tube wall temperature pitch diameter shell diameter Baffle spacing

Hydraulic diameter (Fig. 5.1) de =

5.4.9

      

p2t −πd2o /4 πdo

for square pitch

0.87p2t /2−πd2o /8 πdo /2

for equilateral triangular pitch

Pressure drop µ

Ds ∆p = 4f d where

¶Ã

ρu2 2

 0.3164   Re0.25

f = 

64 Re

!µ

Re

L lb

¶Ã

µ µw

!−0.14

,

(5.8)

≥ 2320

Re < 2320 .

L=tube length lB = baffle spacing. The term (L/lB ) is the number of times the flow crosses the tube bundle=(NB + 1). Where NB is the number of baffles. Dr. Ali A. Rabah, Dept of Chemeng, U of K, Email : [email protected]

5.5 Design Algorithm

5.5

79

Design Algorithm

Step1 Specification Define duty Q Make energy balance if needed to calcualted unspecified flow rates or temperature Q=Mccpc(Tc2-Tc1)=MhCph(Th1-Th2)

Step 9 Estimate tube-side heat transfer coefficient Step 10 Decide baffle spacing and estimate shell side heat transfer coefficient

Step2 Calculate physical properties

Step 11 Calculate overall heat transfer Coefficient including fouling factors Uo,cal

Step3 Assume value of overall coefficient Uo,ass Step 4 Decide number of shell and tube passes Calculate ∆Tlm, F and ∆Tm

No Set Uo,ass=Uo,cal

0 1.6 × 104 where

à −3

hn1 = 7.4 × 10

hn2 Ã

Pe =

wm b , Rem = νL

kL = 0.087 b

Ã

kw kL

kw kL

!0.15 −1/3

P e0.6 Kp0.5 P rL Ã

!0.09

Re0.6 m

!

ρG ρL

"

Ã

!#

(A.65)

P rL ,

(A.66)

!0.2

qb p , Kp = q , b= ∆hV ρG aL σg(ρL − ρG )

m ˙ ρL wm = 1+x −1 ρL ρG

,

1/6

s

2σ , g(ρL − ρG )

qb , Re∗ = , ∆hV ρG νL

NCB

Rem = Re∗

(A.67)

Ã

!

ρL . ρG (A.68)

Dr. Ali A. Rabah, Dept of Chemeng, U of K, Email : [email protected]

142

A Heat transfer coefficient

A.3.10 Jung et al. [64] correlation The Jung et al. [64] correlation is a modified form of the Chen [19] correlation. The convection heat transfer coefficient is calculated using the Dittus-Boelter [33] correlation (equation A.51) and the nucleate part is calculated from the Stephan and Abdelsalm in VDI-W¨armeatlas [157] correlation as "

kL q(b.d) ˙ hn = 207 b.d kL Ts where

#0.745 Ã

ρG ρL

!0.581

Ã

0.533 PrL ,

2σ (b.d) = 0.511 g(ρL − ρG ) µ

1 F = 2.37 0.29 + Xtt   

S= 

A.4

4048Xtt1.22 Bo1.13

(A.69)

!0.5

,

(A.70)

¶

,

(A.71)

Xtt < 1 .

2.0 − 0.1Xtt−0.28 Bo−0.33 1 ≤ Xtt ≤ 5

Two phase flow: Mixture

A.4.1 Steiner [140] correlation Steiner [140] has extended his pure component asymptotic model to mixture. The nucleate part of the heat transfer coefficient is suppressed using the Schl¨ under [126] suppression factor for the nucleate boiling. The Schl¨ under [126] suppression factor is based on the heat and mass transfer laws it is defined as (

"

hid,n Bo q Fn = 1 + (Tb,k − Tb,j )(yej − xej ) 1 − exp q˙ ρL ∆hV βL

#)

,

(A.72)

where Tb is the saturated (boiling) temperature of the pure component, the index j and k stands for the more volatile and less volatile component respectively. βL /B0 = 5 × 105 is the mass transfer coefficient. The ideal nucleate boiling heat transfer coefficient for a mixture hid,n is calculated from the heat transfer coefficient of pure components as "

hid,n =

X x ei

#−1

,

hi,n

(A.73)

and Bo /βL = 5.103 and ρL and ∆hV is the ideal density and enthalpy of evaporation of the mixture respectively. xe and ye is the liquid and vapor mole fraction of the more volatile component respectively. The same approach applies also to the convective part for the liquid-liquid immiscible mixture. That is to say for a liquid-liquid miscible mixture the convective suppression factor made analogous to that for the nucleate boiling heat transfer coefficient as (

"

Bo q hid,c (Tb,k − Tb,j )(yej − xej ) 1 − exp Fc = 1 + q˙ ρL ∆hV βL

#)

.

(A.74)

Dr. Ali A. Rabah, Dept of Chemeng, U of K, Email : [email protected]

A.4 Two phase flow: Mixture

143

A.4.2 Kandlikar [71] correlation Kandlikar [71] has extended his pure component correlation (Kandlikar [70]) to mixtures as • Region I: Near-azeotropic region h = max(hn , hc ) ,

(A.75)

where hn and hc is obtained from equation A.77 and equation A.47 respectively using the mixture properties. • Region II: Moderate diffusion-induced suppression region h = hc ,

(A.76)

where hc is given by equation A.77 with the properties of the mixture. • Region III: Severe diffusion-induced suppression region: 0.03< V1 < 0.2 and Bo ≤ 1E −4 ; V1 ≥ 0.2 h = 1.136Co−0.9 (1 − x) ˙ 0.8 hL0 f (FrL0 ) + 667.2Bo0.7 (1 − x) ˙ 0.8 FF l hL0 FD , where

"µ

V1 =

cpL ∆hV

¶µ

a D12

FD =

¶0.5

Ã

dT |ye − xe| dxe

0.678 . 1 + V1

(A.77)

!#

,

(A.78)

(A.79)

A.4.3 Bennett and Chen [8] correlation Bennett and Chen [8] has extended the Chen [19] correlation (equation A.50) for mixture. Here both the convective and the nucleate parts are suppressed. The convection part which is calculated for the original Chen [19] correlation with mixture properties is suppressed using the following suppression factor Fc =

Tw − Tph , Tw − Ts

(A.80)

where Tw , Tph , and Ts is the wall, equilibrium temperature and saturation temperature respectively. The nucleate part is also calculated using the original Chen [19] model for the pure substance with mixture properties. It suppressed using the the suppression factor given by equation A.79. A.4.4 Palen [111] correlation Palen [111] has extended the original Chen [19] correlation for pure component (equation A.50) to mixture similar to the Bennett and Chen [8] correlation. However, only the nucleate part is suppressed using the following suppression factor Fd = exp(−0.027∆Tbp ) ,

(A.81)

where ∆Tbp is difference between the dew and bubble point temperature of the mixture. Dr. Ali A. Rabah, Dept of Chemeng, U of K, Email : [email protected]

144

A Heat transfer coefficient

A.4.5 Jung et al. [64] correlation Jung et al. [64] have extended their pure substance correlation to the mixture. The nucleate boiling heat transfer coefficient is replaced by the ideal one given by equation A.73. The convective part is suppressed using the following suppression factor Fc = 1.0 − 0 − 35|ye1 − xe1 |1.56 .

(A.82)

For the nucleate part the following suppression factor is employed Fn = where

1 , {[1 + (b2 + b3 )(1 + b4 )](1 + b5 )}2 Ã

1.01 − xe1 b2 = (1 − xe1 ) ln 1.01 − ye1    

!

Ã

xe1 + xe1 ln ye1

0

!

+ |ye1 − xe1 |1.5 ,

Ã

p b4 = 152 pc,1 b5 = 0.92|ye1 − xe1 |

,

!0.66

, Ã

e x1 =1 e y1

(A.84)

x1 ≥ 0.01

b3 =  ³ ´ 0.1  e x1  − 1 xe1 < 0.01 e y1

and

(A.83)

0.001

p pc,1

(A.85) !0.66

,

(A.86)

for xe1 = ye1 = 0 ,

xe1 and ye1 is the liquid and vapor mole fraction of the more volatile component respectively. p and pc,1 is system pressure and critical pressure of the more volatile component respectively.

Dr. Ali A. Rabah, Dept of Chemeng, U of K, Email : [email protected]

145

B B.1

Pressure drop Single phase

The pressure drop due to friction exists because of the shear stress between the fluid and the tube wall. Estimation of the friction pressure drop is somewhat more complex and various approaches have been taken, for example the frictional pressure gradient is given as à ! 4τo 4f m ˙2 dp = = , (B.1) − dz f d 2dρ where m ˙ is the mass flux in kg/m2 s and f is the friction factor calculated using a Blasiustype model as  0.3164   Re0.25 Re ≥ 2320 f=   64 Re < 2320 . Re Integration of equation B.1 yields ∆p =

B.2

4f m ˙2L , 2ρ d

(B.2)

Two phase

In flow boiling, the temperature drops in the direction of flow as a result of the pressure drop. This results in a change in the driving force (temperature difference) for the heat transfer along the flow path. Thus beside the heat transfer coefficient, knowledge of the pressure drop is of paramount importance in the design of the evaporator. In the present work the pressure drop is measured simultaneously with the heat transfer coefficient along the test section. The momentum balance implies that the two phase pressure gradient is composed of three components as à ! à ! à ! dp dp dp dp = + + , (B.3) dz dz f dz a dz h where dp/dz, (dp/dz)f , (dp/dz)a and (dp/dz)h is the total, friction, acceleration and hydrostatic pressure gradient respectively. For a horizontal tube the hydrostatic pressure gradient diminishes. The acceleration pressure drop is caused by the change in momentum in both the liquid and vapor phases. The change in the momentum stems from the change in the velocity of the two phases, which is brought about by the added (or withdrawn) heat to/from the test section. For the case of adiabatic flow the acceleration pressure drop diminishes for ∆pa /ps → 0 (Baehr and Stephan [3]), where ps is the saturation pressure. There exist in the literature a number of approaches for modelling the change in the static pressure drop due to acceleration. The most widely accepted models include homogenous or separated flow models. The separated flow model is also widely known as the heterogenous model. In the homogenous model the static pressure drop due to acceleration is " à ! # à ! 1 1 1 dp 2 d =m ˙ x˙ − + . (B.4) − dz a dz ρL ρG ρL The energy balance in a small unit length dz along the test tube yields 4q˙ dx˙ = . dz m∆h ˙ vd

(B.5)

Dr. Ali A. Rabah, Dept of Chemeng, U of K, Email : [email protected]

146

B Pressure drop

Substitution of equation B.5 into equation B.4 yields the pressure drop due to acceleration as à ! 4q˙m ˙ ρG ∆pa = 1− ∆L . (B.6) d∆hv ρG ρL In the separated flow model the static pressure drop due to acceleration can be derived from the momentum balance as Ã

dp − dz

!

"

d x˙ 2 (1 − x) ˙ 2 =m ˙ + dz ερG (1 − ε)ρL 2

a

#

.

(B.7)

Integration of equation B.7 between the inlet i and outlet o of the test section yields "

−∆pa = −(po − pi )a = m ˙

2

(1 − x˙ o )2 x˙ 2i (1 − x˙ i )2 x˙ 22 + − − εo ρG,o (1 − εo )ρL,o εi ρG,i (1 − εi )ρL,i

#

.

(B.8)

The void fraction ε may be obtained using the Rauhani [117] model which is given as: (

Ã

!

1/4 x˙ x˙ 1 − x˙ 1.18(1 − x)[gσ(ρ ˙ L − ρG )] ε= (1 + 0.12(1 − x)) ˙ + + 1/2 ρG ρG ρL mρ ˙ L

)−1

,

(B.9)

where ρL and ρG is the liquid and vapor density respectively, which are calculated from the fundamental equation of state of Tillner-Roth and Baehr [152] for R134a. g is acceleration due to gravity, σ is the surface tension, m ˙ is the mass flux and x˙ is the quality. The surface tension is calculated using the method of Lucus [92] given in VDI-W¨armeatlas [157]. The pressure drop due to friction exists because of the shear stress between the fluid and the tube wall. Estimation of the friction pressure drop is somewhat more complex and various approaches have been taken, for example in homogenous or separated flow models. In the homogenous model the frictional pressure gradient is given as Ã

dp − dz

!

= f

2ξ m ˙2 4τo = , d dρH

(B.10)

where ξ is the two phase friction factor calculated by a Blasius-type model as ξ=

 0.3164   Re0.25  

64 Re

Re

≥ 2320

Re < 2320 .

and the homogenous densityρH is given as 1 − x˙ x˙ 1 = + . ρH ρL ρG

(B.11)

The two phase Reynolds number Re is Re =

md ˙ , ηT P

(B.12)

where ηT P is a two-phase viscosity. A variety of methods have been proposed to calculate the two phase viscosity, a commonly used one being that proposed by McAdams et al. [95] 1 ηT P

=

1 − x˙ x˙ + , ηL ηG

(B.13)

Dr. Ali A. Rabah, Dept of Chemeng, U of K, Email : [email protected]

B.2 Two phase

147

where ηL and ηG are the liquid and vapor viscosity. In the separated flow model the two phase frictional pressure drop is related to that for single phase as à à ! ! dP dp = ΨG/L , (B.14) dz f dz f,L/G where Ψ is the two phase multiplier. There exist a number of correlations for the prediction of Ψ. These include Friedel [42], Chishlom [22] and Lockhart and the Martinelli [91] model. These models are presented in Appendix B. There exists a number of correlations for the prediction of the two phase multiplier Ψ of the separated flow model. These models are presented in the following subsections. B.2.1

Friedel [42] model ΨL0 = E +

3.24F H F r0.045 W e0.035

,

(B.15)

where E = (1 − x) ˙ 2 + x˙ 2

ρL fG0 , ρG fL0

(B.16)

F = x˙ 0.78 (1 − x) ˙ 0.24 , Ã

H=

ρL ρG

!0.91 Ã

µG µL

Fr =

!0.19 Ã

µG 1− µL

(B.17) !0.7

,

m ˙2 , gdρ2H

(B.18) (B.19)

m ˙ 2d , (B.20) σρH d is tube diameter, σ is the surface tension and %H is the homogenous density given by equation B.11. fG0 and fL0 are the friction factors defined by a Blasius-type model as We =

fL0/G0 =

0.079 , Re0.25 L0/G0

(B.21)

where Re = md/µ. ˙ The range of the validity of the Friedel [42] model is µL /µG < 1000 B.2.2 Lockhart and Martinelli [91] model In the Lockhart and Martinelli [91] model the two phase friction multiplier is C 1 + 2 , X X

(B.22)

2 ψG = 1 + C.X + X 2 ,

(B.23)

ψL2 = 1 +

where X is the Martinelli parameter and the value of the coefficient C is given in Table B.1. The range of the applicability of the Lockhart and Martinelli [91] correlation is µL /µG >1000 and m ˙ 1000 and m ˙ > 100 kg/m2 s. B=

Dr. Ali A. Rabah, Dept of Chemeng, U of K, Email : [email protected]

149

C

Physical properties

The fluid physical properties required for heat exchanger design are divided in thermodynamic and trasport properties. The transport properties include viscosity, thermal conductivity, surface tension and diffusion coefficient are generally calculated from the existing correlations (Pery and Coulson). The thermodynamic properties include demsity, specific heat temperature, pressure (vapor), enthalpy, latent heat of evaporation. Beside the fluid properties the thermal conductivity of the material is necessary for the evaluation of heat transfer coefficient. The thermodynamic properties are evaluated using critical tables.

C.1

Physical properties: Pure fluid

C.1.1 Specific heat The specific heat of the ideal gas is given in as Cp = CP V AP A + (CP V AP B)T + (CP V AP C)T 2 + (CP V AP D)T 3

(C.1)

Where T is in K and CPVAPA, CPVAPB, CPVAPC, CPVAPD are constant in ideal gas heat capacity. These constant are given in Appendix A for organic and inorganic compounds. C.1.2 Vapor pressure The vapor pressure is generally predicted using Antonie equation as ln p = AN T A −

AN T B T + AN T C

(C.2)

where T is in K and ANTA, ANTB,ANTC are Anonie equation constant. These constant are given in Appendix D for organic and inorganic compounds. C.1.3 Liquid viscosity The liquid viscosity is given as: µ

1 1 log µ = V ISA − T V ISB

¶

(C.3)

where VISA, VISB are constants in the liquid viscosity equation. These constant are given in Appendix D for organic and inorganic compounds. C.1.4 Vapor dynamic viscosity VDI-W¨ armeatlas [157] Lucas and Luckas [92] in VDI-W¨armeatlas [157] have recommended the following procedure for the calculation of the vapor viscosity. η = (ηξ)r Fp FQ

1 , ξ

(C.4)

for Tr ≤ 1 and pr ≤ ps /pc

with

(ηξ)r = 0.600 + 0.760pαr + (6.990pβr − 0.6)(1 − Tr ) ,

(C.5)

and β = 1.390 + 5.746pr , α = 3.262 + 14.98p5.508 r

(C.6)

Dr. Ali A. Rabah, Dept of Chemeng, U of K, Email : [email protected]

150

C Physical properties

for 1≤ Tr ≤ 40 and 0≤ pr ≤ 100

"

ApE r (ηξ) = (η ξ) 1 + −1 BpFr + (1 + CpD r ) r

o

#

,

(C.7)

where η o is the low pressure viscosity given as η o ξ = [0.807Tr0.618 − 0.357 exp(−0.449Tr ) + 0.340 exp(−4.058Tr ) + 0.018]Fpo FQo , (C.8) and ξ is given as [Tc ]1/6 [R]1/6 [Na ]1/3 ξ= , (C.9) [M ]1/2 [pc ]2/3 where Na is the Avagadro number in kmol. The coefficients of equation C.7 are given as a1 A = exp(a2 Trγ ) , (C.10) Tr B = A(b1 Tr − b2 ) , (C.11) c1 C = exp(c2 Trδ ) , (C.12) Tr d1 D = exp(d2 Tr² ) , (C.13) Tr E = 1.3088 , (C.14) ς F = f1 exp(f2 Tr ) . (C.15) The coefficients a, b, c, d, e, and f are given in Table C.1 Table C.1. Coefficients of the correlation used for the prediction of the vapor dynamic viscosity.

a1 b1 f1

1.245.10−3 1.6553 0.9425

a2 b2 f2

5.1726 1.2723 −0.1853

c1 d1 ς

Fp = 1 +

(Fpo

0.4489 c2 1.7368 d2 0.4489 ² "

and

"

(ηξ)r − 1) ηoξ #−1

3.0578 2.2310 -7.6351

γ δ

-0.3286 -37.7332

#−3

, "

Ã

(C.16) !#4

(ηξ)r (ηξ)r FQ = 1 + − 1) − 0.007 ln , (C.17) ηoξ ηoξ where Fpo and FQo is low-pressure polarity and quantum factors respectively. These factors are Fpo = 1 , 0 ≤ µr < 0.022 , (C.18) (FQo

Fpo = 1 + 30.55(0.292 − Zc )1.7 , 0.022 ≤ µr < 0.075 ,

(C.19)

Fpo = 1 + 30.55(0.292 − Zc )1.7 (|0.96 + 0.1(Tr − 0.7)|) , 0.075 ≤ µr , (C.20) o where Zc is the critical compressibility factor and FQ = 1.0 for all substances other than He, H2 and D2 . The reduced dipole moment µr is given as µr =

µ2 pc , (kTc )2

(C.21)

where the dipole moment µ for the gases is given in VDI-W¨armeatlas [157] Dr. Ali A. Rabah, Dept of Chemeng, U of K, Email : [email protected]

C.1 Physical properties: Pure fluid

151

C.1.5 Dynamic viscosity of Fenghour et al. [40] The functional form of the liquid and vapor viscosity of ammonia as given by Fenghour et al. [40] is η = ηo (T ) + η1 (T )ρ + η2 (ρ, T ) , (C.22) The first term of the expansion is the dilute gas term which is given as ·

¸

f T )1/2 0.021357 (M ηo (T ) = 100 , 0.29572 exp(Ω)

(C.23)

f is the molecular weight in g/mol, T is the temperature in K. The collision where M integral Ω is defined as (

Ã

kT Ω(T ) = C(1) + C(2) log ²

!

"

4 X

Ã

kT + C(n) log ² n=3

!#n )

,

(C.24)

where ²/k=386 K and the value of the coefficient C is given in table C.2. Table C.2. Coefficients for the Collision integral Ω (equation C.24).

C(1)

4.9931822

C(2) -0.61122364

C(3) 0.18535124

C(4) -0.1116094

The second term of equation C.22 represents the contribution of the moderately dense fluid η1 (T ) = Fv (T )ηo (T )ρ , where

  

13 X

 

i=2

Fv (T ) = C A(1) +

"

Ã

A(i) log

(C.25)

 !# −(i−1)   2 kT

²

 

,

(C.26)

where C=0.6022137/0.29573 and the value of the coefficient A is given in table C.3 Table C.3. Coefficients of equation C.26.

i

A

i

A

1 3 5 7 9 11 13

-0.17999496×101 -0.53460794×103 -0.13019164×105 -0.58711743×105 -0.59834012×105 -0.12027350×105 -0.120807957×103

2 4 6 8 10 12

0.466692621×102 0.33604074×104 0.33414230×105 0.71426686×105 0.33652741×105 0.24348205×104

The third term in the viscosity equation C.22 is the contribution of the dense gas η2 (ρ, T ) =

3 X

F (i, T )ρi+1 ,

(C.27)

i=1

Dr. Ali A. Rabah, Dept of Chemeng, U of K, Email : [email protected]

152

C Physical properties

where

 ³ ´2 ³ ´4 ² ² −1   1 0.219664285 − 0.83651107 × 10  kT kT       ³ ´   ² −2 −2   2 0.17366936 × 10 − 0.83651107 × 10  kT 

F (i, T ) = 

³ ´2 ³ ´3   ² ² −3 −3  3 0.167668649 × 10 − 0.149710093 × 10 +   kT kT       ³ ´4    0.77012274 × 10−4 kT²

The Fenghour et al. [40] correlation for the vapor viscosity of ammonia has an uncertainty of 2% in the temperature range of T < Tc . C.1.6 Surface tension Lucas and Luckas [92] in VDI-W¨armeatlas [157] have recommended the following correlation for the calculation of the surface tension µ ¶m 2/3 1/3 1 − Tr σ = pc Tc b, (C.28) a where the reduced pressure and temperature are defined as pr =

p T , Tr = , , pc Tc

(C.29)

respectively. For a polar fluid like R134a the following quantities are valid a b m X

= = = =

1, 0.1574 + 0.359ω − 1.769X − 13.69X 2 − 0.510ω 2 + 1.298ωX , 1.210 + 0.5385ω − 14.61X − 32.07X 2 − 1.656ω 2 + 22, 03ωX , lgpsr (Tr = 0.6) + 1.70ω + 1.552 .

(C.30) (C.31) (C.32) (C.33)

where ω is the acentric factor and it is given by Pitzer in VDI-W¨armeatlas [157] as The surface tension given by equation C.28 is in 10−5 N/cm. Its level of uncertainty as given by Reid et al. [118] is 1.2 % in the range of the reduced temperature of 0.56 ≤ Tr ≤ 0.63. C.1.7

Thermal conductivity for liquids µ

¶

ρ 1/3 k = 3.65 × 10 Cp . (C.34) M where k thermal conductivity W/moC, M is the molecular mass, Cp speific heat capacity 3 (kJ/kg oC), ρ density (kg/m ) −5

C.1.8

Thermal conductivity for gases µ

¶

10.4 . (C.35) M where k thermal conductivity W/m o C, M is the molecular mass, Cp specific heat capacity (kJ/kg o C), µ viscosity in (mNs/m2 ) k = µ Cp +

Dr. Ali A. Rabah, Dept of Chemeng, U of K, Email : [email protected]

C.2 Physical properties: Mixture

153

C.1.9 Specific enthalpy For the vapor phase, the deviation of the specific enthalpy from the ideal state can be illustrated using Redlich-Kwong equation written as z 3 + z 2 + z(B 2 + B − A) = 0 .

(C.36)

where z is the compressibilty factor defined as pv . RT

z= and A=

aP

h = ho + RT +

C.2

,B =

R2 T 2.5

(C.37) bp . RT

Z v "Ã 0

dP T 2 2.5 R T dT

(C.38)

!

#

− p dv .

(C.39)

Physical properties: Mixture

C.2.1 Liquid dynamic viscosity of mixtures For a liquid mixture which contains one or more polar constituents Reid et al. [118] recommended the following model for the calculation of the mixture liquid viscosity ln ηm =

n X

xi . ln ηL,i + 2.xe1 .xe2 .G12 ,

(C.40)

i=1

where xei is the mole fraction of the component i, ηL,i is the viscosity of the component i in kg/ms and G12 is an adjustable parameter normally obtained from experimental data. For a polar-nonpolar mixture G12 = -0.22. The Reid et al. [118] model give the thermal conductivity with a mean error of less then 5%. C.2.2 Vapor dynamic viscosity of mixtures The viscosity of a gas mixture can be approximated by using the principle of the kinetic theory (Reid et al. [118]) as o ηm = ηm + ∆η , (C.41) o where ηm is the mixture gas viscosity at a low pressure and ∆η is a correction factor for the high pressure viscosity n X yei ηG,i o , (C.42) ηm = Pn ei φij j=1 y i=1

where yei is the mole fraction of the component i and ηi is the viscosity of the pure component i. φij is a parameter which may be estimated as h

φij =

f /M f )0.25 1 + (ηG,i /ηG,j )0.5 (M j i f /M f )]0.5 [8(1 + M i j

φji =

f ηG,j M j φ . f ij ηG,i M i

i2

,

(C.43)

(C.44)

Dr. Ali A. Rabah, Dept of Chemeng, U of K, Email : [email protected]

154

C Physical properties

The high pressure correction term is estimated as i

h

∆η =

0.497.10−6 exp(1.439ρr,m ) − exp(−1.111ρ1.858 r,m ) 1/6

−2/3

f −0.5 pc,m Tc,m M m

.

The pseudo critical properties of the mixture are calculated as X X X pc,j υc,j Tc,m = yej Tc,j , υc,m = yej υc,j , Zec,j = , Zem = yj Zec,j , RT c,j j=1 j j f = M m

X

f, yej M j

ρc,m =

j=1

f /1000 M m , υc,m

ρr,m =

ρm , υc,m

pc,m =

(C.45)

(C.46)

RTc,m Zec,m , (C.47) υc,m

where T is in K, p is in Mpa, υc,m is in m3 /kmol, ρr,m is in kg/m3 , M is in g/mol and ηm is in kg/ms. The error associated with this model is seldom exceeded 3 to 4% (Perry and Green [112]). C.2.3 Liquid thermal conductivity of mixtures Reid et al. [118] have recommended a Filippov-like model for the prediction of the thermal conductivity of a liquid mixture as λm =

2 X

f λ − 0.72X X f X i L,i 1 2 |λL,2 − λL,1 | ,

(C.48)

i=1

f and X f is the weight fraction of the component 1 and 2 respectively and λ and where X 1 2 1 λ2 is the thermal conductivity of the component 1 and 2 in W/mK respectively.

C.2.4 Vapor thermal conductivity of mixtures The thermal conductivity of a low-pressure gas mixture can be determined from the relationship given by Reid et al. [118] λG,m =

n X

yei λG,i , Pn ei Aij j=1 y i=1

(C.49)

where λG,m is the low-pressure gas mixture thermal conductivity, λG,i is the low-pressure thermal conductivity of the pure component i. For a binary mixture of two non-polar gases or a non-polar and a polar gas, Aij may be calculated by the model given by Perry and Green [112] as h i c /M f )0.25 2 1 + (λtr,i /λtr,j )0.5 (M j i Aij = , (C.50) f /M f )]0.5 [8(1 + M i j with Γj exp(0.0464Tr,i ) − exp(−0.2412Tr,i ) λtr,i = , (C.51) λtr,j Γi exp(0.0464Tr,j ) − exp(−0.2412Tr,j ) f is the molecular weight and Γ is defined as where M "

f3 Tc,i M i Γi = 210 Pci4

#(1/6)

,

(C.52)

f is in g/mol and λ is in W/mK. This model yields an error where T is in K, p is in bar, M of less than 5% in the prediction of the thermal conductivity of the gas mixture.

Dr. Ali A. Rabah, Dept of Chemeng, U of K, Email : [email protected]

C.3 Software packages

155

C.2.5 Surface tension of mixtures Lucas and Luckas [92] in VDI-W¨armeatlas [157] recommended the following method for calculation of the mixture surface tension µ

σm = where

2/3 1/3 pc,m Tc,m

1 − tr,m am

¶nm

bm ,

(C.53)

#

"

X Ts,ri ln(pc,m /1.01325) , bm = xei bi , bi = 0.1196. 1 + 1 − Ts,ri

am = 1, nm = 11/9, Tc,m =

X

xei Tc,j , υc,m =

X

j=1

Zem =

X j

xj υc,j , Zec,j =

j

xej Zec,j ,

pc,m =

RTc,m Zec,m , υc,m

(C.54)

pc,j υc,j , RTc,j

Ts,ri =

(C.55)

Tb,i , (C.56) Tc,i

where Tb,i =T (p=1.01325 bar) is the normal boiling point temperature of the pure component i. T is in K, p is in bar and σ is in N/m. The Lucas and Luckas correlation yields an error of