Experimental and Theoretical Study of Reflux Condensation

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Portions of this document may be illegible in electronic image products. Images are produced from the best available original document. Experimental and Theoretical Study of Reflux Condensation

Knut Bakke

Thesis submitted in partial fulfillment of the requirements for the degree of

Doktor Ingenipr

Norwegian University of Science and Technology Department of Refrigeration and Air Conditioning

November 1997 “Experience is the name everyone gives to their mistakes.”

Oscar Wilde Abstract

The objective of this work is to study separation of gas mixtures in a reflux condenser, also called a dephlegmator. Reflux condensation is separation of a gas mixture, in reflux flow with condensing liquid, under continuous heat removal. This thesis con tains theoretical and experimental work on the subject. A numerical model of a dephlegmator for binary mixtures was developed. The model may readily be extended to multi-component mixtures, as the solution method is based on a matrix solver. Separation of a binary mixture in a reflux condenser test rig is demonstrated. The test facility contains a single-tube test section, and was designed and built during this project. Test mixtures of propane and n-butane were used, and a total of 15 experi ments are reported. Limited degree of separation is obtained in the experiments, due to limited heat transfer area and narrow boiling point range of the test mixture. The numerical model reproduces the experiments, within reasonable accuracy. Devi ation, between measured and calculated properties, is less than 6% of the measured temperature, and less than 5% of the measured flow rate. The model work is based on mechanistic models of physical processes, and has not been calibrated or tuned to fit the experimental data. The numerical model is applied on a number of separation processes. These case studies show that the required heat transfer area increases rapidly with increments in top product composition (light component). Flooding limits the amount of reflux liquid. The dephlegmator is, therefore, suitable for separation of feed mixtures that are rich in light components. The gliding temperature in the dephlegmation process enables utilisation of top product as refrigerant, with subsequent energy savings as a result.

i ii Preface

This work was accomplished at Department of Refrigeration and Air Conditioning at the Norwegian University of Science and Technology (NTNU). The study started in September 1994, and ended in November 1997. The thesis is a contribution to the research and development activity on process equipment for treatment of natural gas, and was financed by the Research Council of Norway (NFR), through the research program “GAVOT”, Gassforskning - varer og tjenester. My supervisors have been Associate Professor Geir A. Owren, NTNU and Researcher Bengt A. Neeraas, SINTER During this time, I have been employed by the Foundation for Scientific- and Indus trial Research, SINTER. Additional financial support provided by SINTER and NFR made it possible to per form experimental research, as a test facility was built in the laboratory. Research manager David Lysne was very positive and helpful in the process of financing the experimental activity. I would like to express my thankfulness to Geir Owren for fruitful and interesting discussions on all aspects of this work. It has truly been an experience. Further, thanks are due to colleges at NTNU - SINTER for making this department an interesting place to spend time. More specific, thanks are due to Arvid Almen- ning and Karl Gustav Gustavsen who gladly assisted me in the laboratory. Morten Christian Svensson helped me with the data reconciliation method. Tove Stoeckert and David Lysne volunteered to proofread the thesis. Without the positive attitude of these people, this work would have been much harder than it turned out to be. Finally, many thanks to friends and family, who put up with me through this chal lenging period.

Trondheim, November 1997

Knut Bakke

m iv Contents

Abstract i

Preface ili

Nomenclature xi

1 Introduction 1 1.1 Background ...... 1 1.2 Structure of the thesis...... 2 1.3 Limitations ...... 3 1.4 Definitions ...... 3

2 Literature review 5 2.1 Heat- and mass transfer models ...... 5 2.2 Flooding point prediction ...... 8 2.3 Processes utilising dephlegmator technology ...... 13

3 Theory 17 3.1 Multicomponent heat-and mass transfer...... 17 3.2 Flooding ...... 19 3.3 Pressure dependence and pressure drop ...... 20

4 Numerical model 25 4.1 Model basis and assumptions ...... 25 4.2 Model implementation for an arbitrary heat exchanger ...... 30 4.3 Model implementation for PFHE...... 31 4.4 Comparison with other models ...... 37

5 Test facility 39 5.1 Design ...... 39 5.2 Instrumentation ...... 46

6 Experimental procedure 51 6.1 Selection of test fluid...... 51 6.2 Operation ...... 53 6.3 Data collection and conversion ...... 53 6.4 Parameter estimation ...... 54

v 7 Results 59 7.1 Experimental results ...... 59 7.2 Experimental results compared with numerical calculations ...... 63 7.3 Discussion ...... 65

8 Case studies using the numerical model 73 8.1 General case study description ...... 73 8.2 De-methanizer...... 74 8.3 De-ethanizer...... 84 8.4 De-propanizer ...... 86 8.5 Alternative design of plate-fin layer ...... 88

9 Recommendations for future work 91

10 Conclusions 93

References 95

Appendices 101

A Patents using dephlegmator technology 103

B Matrix elements in model solution procedure 107

C Gas chromatograph measurements 111

D Accuracy in Peng-Robinson and Soave-Redlich-Kwong cubic equations of state for propane—n butane mixtures 115

E Estimation and treatment of uncertainty in measurements 121

F Data analysis of measurements 125

G Summary of measurements 129

H Specific recommendations for future work 163

vi List of Tables

1.1 Definitions ...... 3 3.1 Data for pressure drop calculation (Measurement 1100697)...... 23 4.1 Initial value input to numerical model ...... 29 4.2 Plate-fin dephlegmator design - parameter range ...... 36 5.1 Accuracy of instrument Bopp & Reuther type OI 06Agl9 R7/A4 47 5.2 Calibration of instrument EG&G type FT2-8WFR2-PEH1 ...... 49 6.1 Test rig fluid mixture composition ...... 52 6.2 Control utilities on test rig ...... 53 7.1 Operating range of test rig ...... 59 7.2 Effect of heat- and mass transfer coefficient (Average deviation be tween measured- and calculated values in percent of measured value) 68 7.3 Estimated sub-cooling, due to difference in predicted and saturated liquid composition, and difference in measured- and calculated tem perature ...... 70 7.4 Effect of initial value, vapor flow rate (Average deviation between measured- and calculated values in percent of measured value) ... 72 8.1 Base case input data for de-methanizer case...... 75 8.2 Design of dephlegmator (De-methanizer case)...... 76 8.3 Effect on design of parameter variation ...... 77 8.4 Sensitivity of de-methanizer design to process pressure ...... 79 8.5 Sensitivity of de-methanizer design to wall heat flux...... 80 8.6 Sensitivity of de-methanizer design to top product composition (methane) 81 8.7 Distillation column design (Dephlegmator pre-separation, 15 trays) . 82 8.8 Distillation column design (Without dephlegmator pre-separation, 10 trays) ...... 83 8.9 Design of dephlegmator (De-ethanizer case with 50% capacity) ... 85 8.10 Design of dephlegmator (De-propanizer case)...... 87 C. 1 Gas chromatograph configuration ...... Ill C. 2 Calibration data for GC measurements on Cg/n-C^ ...... 113 D. 1 Comparison of thermodynamic data from experiments [57] and Peng- Robinson EOS ...... 119 D. 2 Comparison of thermodynamic data from experiments [57] and Soave- Redlich-Kwong EOS...... 120 E. 1 Uncertainty in measurements (within a 95% confidence level for ran dom errors) ...... 124 E.2 Probability factors of the T distribution with v degrees of freedom [59] 124

vii F. 1 Summary of variables, measurements and equations in data analysis 127 F. 2 Measurement points on test rig ...... 128 G. l Summary of measurements (1)...... 129 G.2 Summary of measurements (2)...... 130 G.3 Summary of measurements (3)...... 130 G.4 Relative deviation between measured values and model calculations (in percent of measured value)...... 131

Vlll List of Figures

1.1 The principle of reflux condensation ...... 2 2.1 Pressure drop and superficial liquid velocity as a function of superfi cial vapor velocity ...... 8 2.2 Calculated flooding velocity for water at 10 bar in a 20 mm (i.d.) tube 9 2.3 Calculated flooding velocity for methane at 10 in a 20 mm (i.d.) tube 10 3.1 Illustration of the condensing process in a T-x plot (Binary mixture, constant pressure)...... 18 3.2 Mass transfer-diffusion vs. concentration gradient [14] ...... 20 3.3 Total- and gravitational pressure drop in dephlegmator tube as a func tion of void fraction ...... 24 3.4 Pressure drop due to acceleration and friction in dephlegmator tube as a function of void fraction ...... 24 4.1 Control volume for reflux condensation model ...... 25 4.2 Fin geometry of a plate-fin heat exchanger ...... 31 4.3 Sensitivity of PFHE heat transfer area to variation of fin geometry . 34 4.4 Sensitivity of PFHE flooding ratio to variation of fin geometry . . . 35 4.5 Comparison between model results and data from Di Cave et al. [21 ] - condensation ratio and composition ...... 38 5.1 Dephlegmator test rig [53]...... 40 5.2 Connector sheet for power supply unit [54] ...... 42 5.3 Details of test rig - test section ...... 43 5.4 Details of test rig - boiler [53] ...... 44 5.5 Details of test rig - heating cable layout in boiler [53]...... 45 5.6 Temperature reference connection ...... 47 5.7 On-site check of reflux volume flow meter...... 48 6.1 Boiling-point vs. pressure diagram for light hydrocarbons C% —»Cs . 52 6.2 Flow of information in data analysis and model evaluation ...... 54 6.3 Parameter estimation of measured data...... 57 7.1 Experimental results: Variation of separation (propane) with wall heat flux ...... 60 7.2 Experimental results: Variation of reflux ratio with wall heat flux . . 60 7.3 Experimental results: Comparison between predicted and saturated reflux liquid composition (propane) ...... 61 7.4 Statistical uncertainty of liquid volume flow measurements...... 62 7.5 Comparison between measured and calculated temperature ...... 64 7.6 Comparison between measured and calculated feed flow rate .... 64

IX 7.7 Comparison between measured and calculated reflux flow rate ... 65 7.8 Temperature measurement points of vapor inlet and reflux liquid outlet section ...... 66 7.9 Liquid- and vapor temperature deviation as function of Tv>meas - Tl,meas ...... 67 7.10 Saturated liquid composition dependency on temperature for propane/n- butane mixtures at 10 bar pressure ...... 69 7.11 Illustration of sub-cooling in a T-x plot at constant pressure...... 70 7.12 Reduction of heat transfer area with void fraction in a circular tube . 71 8.1 Methane-ethane T-x diagram ...... 74 8.2 Methane - ethane composition profile ...... 77 8.3 Sensitivity of de-methanizer design to process pressure ...... 78 8.4 Sensitivity of de-methanizer design to wall heat flux...... 79 8.5 Sensitivity of de-methanizer design to top product composition ... 80 8.6 Process plant with dephlegmator and distillation column ...... 82 8.7 Partial refrigeration by top product in a dephlegmator ...... 84 8.8 De-ethanizer composition profile ...... 86 8.9 De-propanizer composition profile ...... 88 8.10 New design of PFHE dephlegmator internal geometry ...... 89 C. l Sample of gas chromatograph printout ...... 112 D. l Tuning of PR interaction coefficient, 8^...... 117 D.2 Tuning of SRK interaction coefficient, ...... 117 D.3 Experimental and calculated values using Peng-Robinson EOS with tuned interaction coefficient, Sij = -0.0086 ...... 118 F.l Conceptual sketch of test rig ...... 125

x Nomenclature

Roman letters Unit First introduced A Area 4 A Coefficient matrix 4 B Bypass vapor stream kmole/s F C Constant in Equation 2.4 2 D Tube inside diameter inch 2 D Binary diffusion coefficient m2/s 3 F Correction factors in equation 2.3 2 F Feed flow rate kmole/s 4 F() Set of constraints 6 FR Flooding ratio 4 G Superficial vapor mass flux kg/m 2s (or Ib/h ft2) 2 G Mass flow rate kg/m 2s 3 G Molar flow rate kmole/s 4 Gr Grashof number 2 H Height of plate-fin core m 4 J Molar flux kmole/m 2s 3 L Superficial liquid mass flux kg/m 2s (or lb/h ft2) 2 L Tube length m 3 L Reflux liquid stream kmole/s M Mass kg MW Molecular weight kg/kmole N Molar flux kmole/m 2s N Number of moles kmole Nu Nusselt number P Pressure Pa Pr Prandtl number R Residual vector R Response factor R Universal gas constant (8314.4) J/kmole K

R Return liquid stream kmole/s HOn^-M o^o\wt>uai Re Reynolds number

xi Xll

s Perimeter length m 3 s Precision index of measurement 7 T Temperature K 3 V Top product vapor stream kmole/s 6 w Width of plate-fin core m 4 z Vector of data values 6 a Attraction parameter J/kmole D b Half fin height m 4 b Van der Waals covolume m3/kmole D c Molar concentration kmole/m 3 3 cp Molar heat capacity J/kmole K 4 f Friction factor 3 g Acceleration of the force of gravity m/s2 2 h Enthalpy J/kmole 4 h Fin height m 4 j Dimensionless superficial velocity 2 j Colburn factor 2 k Mass transfer coefficient kmole/m 2 s 4 n Molar flux across interface kmole/m 2 s 4 n Number of fins per meter m-1 4 P Fin spacing m 4 q Heat flux W/m2 4 q Duty W 6 t Probability multiplier E t Thickness m 4 u Velocity m/s (or ft/s) 2 u Velocity vector 3 V Molar reflux ratio 2 V Molar volume D X Solution vector 4 X Variable E x,y,z Molar composition 2,2,6 y Measured value E z Coordinate direction m 2

Experimental and Theoretical Study of Reflux Condensation xiii

Greek letters A Deviation 4 a Heat transfer coefficient W/m2K 3 a Relative volatility 3 a Void fraction 3 Q

a Correction factor in PR and SRK Q 6 Interaction coefficient e Tube wall roughness m 3 e Error estimate m E 8 Tube taper angle (from horizontal) degrees 2 6 Second order error term J/kmole 4 k Correction factor in PR and SRK D A Thermal conductivity W/m2 K 4 jj, Dynamic viscosity Ns/m2 (or cp) 2 V Kinematic viscosity m2/s 3 p Density kg/m 3 (or lb/ft3) 2 a Surface tension N/m (or dyne/cm) 2 a Tensile stress N/tn2 4 a Standard deviation 6 T Shear stress N/m2 3 4> Area factor 4 w Acentric factor D

Subscripts I Interface 2 a Light component in binary mixture 3 abs Absolute value G acc Acceleration 3 b Heavy component in binary mixture 3 boil Boiler 6 bot Bottom 8 bypass Bypass vapor stream F c Cross (perpendicular to flow direction) 4 c Combined E

Experimental and Theoretical Study of Reflux Condensation xiv

calc Calculated value from numerical model 7 col Distillation column 8 cond Condenser 6 deph Dephlegmator 8 ext External refrigeration 8 feed Feed stream to separation unit 4 fin Fin (in PFHE) 4 fric Friction 3 grav Gravity 3 h Hydraulic 2 i,j,k Counting integers 4, C, E in Inlet 2 I Liquid 2 lam Laminar flow 3 loss Heat loss on test rig 6 meas Measured values 7 out Outlet 2 P Plate (in PFHE) 4 pred Indirectly deteminded measurement value 7 r Reduced temperature (= D rect Rectifier section of column 8 ref Reference value 4 reflux Reflux liquid stream 8 strip Stripper section of column 8 sub Sub-cooling 7 sur Surroundings F test Test section 5 top Top product stream from separation unit 4 tot Total 3 turb Turbulent flow 3 V Vapor 2 w Wall 3 V Degrees of freedom E 0 Initial or reference value 4

Experimental and Theoretical Study of Reflux Condensation XV

Superscripts NOC Number of components 3 est Estimate F n Upper counting limit in summation 6 sat Saturated state 4

Miscellaneous symbols d Differential operator 2 Differential vector operator 3 d Partial differential operator 4

Abbreviations APCI Air Products & Chemicals Inc. 2 Ci,C2,C3,...,Cn Hydrocarbons (methane,ethane,butane,etc) 6 EOS Equation of state D GC Gas chromatograph 5 HTFS Heat Transfer and Fluid Flow Services 2 IEA International Energy Agency 1 LNG Liquid natural gas 2 NOC Number of components 3 NGL Natural gas liquids 2 NTNU The Norwegian University of Science and Technology PFHE Plate-fin heat exchanger 1 PR Peng-Robinson EOS C RMS Root mean square 6 SRK Soave-Redlich-Kwong EOS D TEMA Tubular Exchanger Manufacturers Association 5 VLB Vapor-liquid equilibrium D VOC Volatile organic compounds 1 i d. Inner diameter 2

Experimental and Theoretical Study of Reflux Condensation 1 Introduction

1.1 Background

Norway is a major exporter of natural gas, and has increased its export volume sig nificantly during the past few years. The gigantic Troll field1 will, with supplements from other fields, provide a vast export of gas for at least 50 years. In this context, research and development of gas related technology is important for the Norwegian petroleum industry. The International Energy Agency (IEA) strategy plan 1995 - 2000 [1] states, quota tion: “Around 60% of all applications of heat exchangers involve multiphase flow, in nearly all cases with phase change (condensation , evaporation). The inadequacy of design methods in this area still presents major problems, in extending the range of applications ...” Reflux condensation is such an extension to this range of applications. The above mentioned strategy plan also states that extension of plate-fin heat exchanger (PFHE) applications to include simultaneous heat- and mass transfer should be pursued. This thesis presents a separation unit, called a dephlegmator which is designed for separating gas mixtures. The dephlegmator may, in principle, be used for separation of any zeotropic gas mixture. A dephlegmator is essentially a separation process inside a heat exchanger, and it can fully or partly replace conventional equipment, like distillation columns and partial condensers. Reflux condensation works as displayed in Figure 1.1. A mixed vapor stream is continuously stripped of heavy components in up-flow, and the reflux liquid flow is enriched on these components. Continuous heat removal contribute to high thermal efficiency. Small mass transfer driving forces reduce thermodynamic irreversibil ity compared to conventional distillation. Typical processes where dephlegmator technology is potentially viable are petrochemical plants such as ethylene recovery, de-methanizer, de-ethanizer, de-propanizer, pre-separation and retrofitting of existing distillation processes. Other areas are re-liquefaction of boil-off gas from gas tanks and VOC recovery. Current design basis and operational experience are proprietary to the manufactur ers of equipment and processes. Improved understanding and open literature on the subject, will reduce scepticism and enhance utilisation among the users of such equipment, namely the process industries.

1 The Troll gas field was officially opened at the 19 June 1996, and gas exports started in October the same year

1 2 1 INTRODUCTION

! t Vapor

I I t Vapor

Figure 1.1: The principle of reflux condensation

1.2 Structure of the thesis

The philosophy used when undertaking this work was to first identify a particular physical phenomenon to examine in detail. Secondly, the identified phenomenon, being reflux condensation, was examined with respect to the physics involved and translated into a model. The model has subsequently been compared with experi mental data, to ascertain its validity. Finally, the model was used to study processes viable for industrial use. This thesis contains the following main parts:

• Theory: Literature review, theoretic basis and numerical model for dephlegmator simulation in Chapters 2, 3 and 4.

♦ Experimental work: Design, engineering and construction of the test facility in Chapter 5. Measurement program and uncertainty analysis in Chapter 6.

• Results: Comparison between model and experiments. The results are presented in Chapter 7.

♦ Case study: The numerical model is applied to design dephlegmators to different processes in Chapter 8.

Experimental and Theoretical Study of Reflux Condensation 1.3 Limitations 3

• The thesis is completed with recommendations for further work in Chapter 9 and conclusions in Chapter 10.

1.3 Limitations The chosen topic of this thesis is an extensive one, and must be subject to some limitations due to the limited time spent on the work. This three year project includes experimental and theoretical work. Both the model and the experiments consider a single tube, and the work does not reflect on “multi-tube items” such as flow distribution and instability. In Chapter 8, a plate-fin heat exchanger is calculated on an “equivalent ” single tube basis. All model and experimental work have been performed on binary mixtures. The terms dephlegmator and dephlegmation are used in connection with separation using membranes and emergency cooling in nuclear power plants. These subjects are not considered a part of this work, although flooding point prediction methods, de veloped in connection with emergency cooling in nuclear power plants, are reviewed.

1.4 Definitions To avoid any potential confusion with respect to the terms used throughout this thesis, the following definitions are given:

Term Definition Dephlegmation Separation of a gas mixture in reflux flow with condensing liquid under continuous heat removal Dephlegmator An apparatus in which dephlegmation occurs Reflux condensation Dephlegmation Reflux condenser Dephlegmator

Table 1.1: Definitions

Experimental and Theoretical Study of Reflux Condensation 4 1 INTRODUCTION

Experimental and Theoretical Study of ReOux Condensation 2 Literature review

The literature on dephlegmation, or reflux condensation, is concerned with three different areas; heat- and mass transfer, flooding and process integration. Theoretical and experimental development, or a combination of both, are reported. The following sections reviews the open literature. Literature surveys were made both in the database of Heat Transfer and Fluid Flow Services (H ITS), Harwell, UK and other major databases through the Technical University Library of Norway. Some 100 references were found with dephlegmation or dephlegmator as subject, of which 41 are patents. A summary of known patents are listed in Appendix A. Work from countries such as the former USSR, Poland, Romania and China is unfortunately inaccessible due to lack of translations. These are, therefore, only reviewed on basis of abstracts from the databases [2,3]. References of direct relevance to the topics discussed in this thesis are cited where appropriate.

2.1 Heat- and mass transfer models

Numerous authors have studied heat- and mass transfer of multicomponent (mainly binary) mixtures. Colburn & Hougen [4] wrote the first significant paper on mul ticomponent condensation. This along with other important work [5-12] forms the basis for the specific work on condensation of mixtures. The subject is also described in various books, where the works by Collier & Thome [13] and Taylor & Krishna [14] are detailed and well described. Articles which particularly deal with heat- and mass transfer in reflux condensation of mixtures are scarce. Kirschbaum [15] presents some early work (1930) on reflux condensation of binary mixtures. This work, along with the work of Kirschbaum & Lipphardt [16] and Kirschbaum & Troster [17] investigates mass transfer in partial condensation. Kirschbaum [15] claims that the rectification is solely dependent on the reflux ratio (v). However, Equation 2.1 is valid only at thermodynamic equilib rium, and denotes an upper separation limit. A rather large deviation between the theoretical limit and experimental data is shown [17]. This deviation increases with vapor velocity and reflux ratio.

(2.1)

5 6 2 LITERATURE REVIEW

The experiments of Kirschbaum et al. were performed on the outside of a single tube, contrary to the common practice of reflux condensation inside tubes. Bell [18] presents an algorithm for design and rating of reflux condensers, but it is neither implemented nor verified experimentally. The author points out the lack of understanding of the processes involved and experimental basis for further develop ment. Two articles by Davis, Tung and Mah [19,20] study condensation and evaporation in reflux flow. In Reference 19, an experimental scheme with a binary mixture of n-hexane - toluene with heat input/removal through a wetted-wall is studied. A math ematical model based on differential conservation equations is presented and verified against experiments. The model includes heat- and mass transfer in both liquid and vapor phase, and performs top-down calculation. Davis et al. assumes uniform liquid composition in the liquid phase. The experimental rectangular column consists of one wetted wall with three adjacent adiabatic, dry walls (0.152mx0.00953m). The model predictions are in good agreement with experiments, but few of the experi mental runs are presented. In Reference 20, the wetted wall column is replaced by plate-fin channels. Again, the authors report acceptable agreement between theory and experiments. Di Cave, Mazzarotta and Sebastani [21] present a model based on the Colburn & Drew [5] approach. The model is supported by experiments on a 18 mm i.d. 920 mm long tube. The authors point out sensitivity of the model with respect to heat- and mass transfer coefficients. The model is developed for a single tube, and it is argued that this is sufficient to describe a complete tube bundle. No comments are made on multi-tube challenges such as fluid distribution, instability or flooding limits. Fox, Peterson and Hijikata [22] present a time dependent hydrodynamic model for steam-air mixtures in the condensing section of a thermosyphon. The oscillating nature of the reflux flow phenomenon at various Reynolds 1 (Re) and Grashof 2 (Gr) numbers are studied. Unstable flow patterns were found, as expected, at increasing Re and Gr numbers. The impact from flow patterns on heat transfer was found to be significant. Heat- and mass transfer coefficients in reflux condensation of mixed vapors are treated by Onda, Sada and Takahashi [23]. An experimental apparatus with 20 mm column i.d. and lengths 330, 830,1330 and 1830 mm is presented. Test fluid is a binary mix

1 Reynolds number denotes the ratio of inertia and viscous forces 2Grashof number denotes the ratio of buoyancy and viscous forces

Experimental and Theoretical Study of Reflux Condensation 2.1 Heat- and mass transfer models 7 ture of methanol and water, No information on temperature or pressure is reported, although an illustration of the experimental apparatus indicates atmospheric condi tions. The apparently good agreement between experiments and theory is, therefore, of limited value to the reader. Rohm [24] treats unsteady state behavior in dephlegmation of binary vapor mixtures. A literature survey by the same author [25], based on several references, states that three known methods for multi-component mass transfer give similar and acceptable results. These methods are the linear theory 3 by Toor [7,8] and Stewart & Prober [9] and the matrix method of Krishna & Standart [11]. The models are compared for steady state simulation of the dephlegmation process on a ternary mixture (methanol, ethanol and water). The matrix method of Krishna & Standart [11] produces more accurate results, the penalty is more computing time. Dixit, Gaitonde and Sharma [26] present a model for computation of rectification in dephlegmators for an aqua-ammonia (binary mixture) refrigeration system. The method is extracted from a general model for distillation columns, and modified for dephlegmation. The authors discuss, rather briefly, the results of computations on a qualitative basis. Verification of these are not reported. Fiolitakis [27] presents a model for binary mixtures. The model consists of conser vation equations for species, mass and energy. At the inlet of the dephlegmator, the author assumes thermodynamic equilibrium (i.e. both temperature and concentration gradients are zero) between liquid and vapor. Urban, Nishio, Matsuo, Ishikawa, Natori, Akamatsu, Sonoi and Onaka [28] present a recent paper about a dephlegmator for an ethylene plant. The authors report a nu merical model and experiments on a pilot plant, with a plate-fin heat exchanger used as a dephlegmator. The described model is detailed, and even distinguish between primary surface (parting sheets) and fin surface. The rationale for this is, quotation: "The separation effect was only slightly better in the case of serrated fins despite much higher value of jo factor. This indicates that condensation of low volatility compo nents with simultaneous vaporization of high volatility components (which results in high separation effect) occurs only at the parting sheet surface. At the fins surface all components are condensing in a “one way” manner. Next, the liquid condensed on the fins moves under surface tension forces towards the parting sheet (primary) surface.” This conclusion is not strongly supported by the reported observations, and the difference in separation may originate from other sources, such as coolant

3The linear theory of multicomponent mass transfer were developed independently by the authors

Experimental and Theoretical Study of Reflux Condensation 8 2 LITERATURE REVIEW conditions and over design of area. The authors report agreement between model and pilot plant test, although no numbers are presented to quantify this agreement. The paper also discuss flow distribution an distributor design. H ITS in the UK works both with theory and laboratory activities on dephlegmators. This work is not commonly available to the public and, thus, not reported in this thesis.

2.2 Flooding point prediction

- dP/dz (

(------)

Figure 2.1: Pressure drop and superficial liquid velocity as a function of superficial vapor velocity

Flooding is recognized as an important constraint in vertical reflux flow. Much of the work on this subject has been dedicated to emergency heat removal in nuclear reactors. Definition of the flooding point varies from author to author. Figure 2.1 shows both liquid superficial velocity and pressure drop plotted qualitatively against superficial vapor velocity in a vertical tube. Some authors define the flooding point based on entrainment level, some on liquid bridging of the flow channel, and others on no liquid reflux. The latter two criteria are recognized in the figure. No liquid reflux occurs in the vicinity of the maximum pressure drop, while bridging occurs when the pressure drop curve starts to increase rapidly towards the peak with increasing superficial vapor velocity.

Experimental and Theoretical Study of Reflux Condensation 2.2 Flooding point prediction 9

Many attempts have been made to predict the flooding point, most of them are based on empiricism. There are several reviews on the flooding literature [29-32], where the review by Bankoff & Lee [32] considers most aspects of flooding. All of the reviews point out that vapor velocity and entrance/exit geometry are significant parameters that determine the onset of flooding. Another point commented is the wide variation in flooding point predictions between different authors. There is no common agree ment on what parameters that are most important to the flooding phenomenon. The difference in experimental setup explains some of the variation. Most experiments are done with air-water or steam-water, different fluids properties may, therefore, influence flooding predictions. Further, it is unclear whether or not the adiabatic and condensing situation differs significantly with respect to the flooding point. Correlations for flooding point prediction are either empirical, semi-empirical or analytical. Ragland [31] states that the statistical nature of this phenomenon may obstruct purely analytical solutions. Many correlations for flooding point prediction exist [29-35], only four are presented here to show the qualitative differences among them. The equations are plotted in Figures 2.2 and 2.3, for a methane and a water system, respectively, at 10 bar in a 20 mm (inner diameter) tube. The differences in predicted flooding velocity are evident.

Flooding velocity (Water (liquid - vapor), 10 bar) 20 i i i i i i i English et al. Diehl and Koppany Wallis (C=1.0) Wallis (C=0.7) I » Pushkina and Sorokin I g. io

_i_ _i_ 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 (L/G) Ratio of superficial liquid to vapor mass flow rates

Figure 2.2: Calculated flooding velocity for water at 10 bar in a 20 mm (i.d.) tube

Experimental and Theoretical Study of Reflux Condensation 10 2 LITERATURE REVIEW

Flooding velocity (Methane (liquid - vapor), 10 bar) 5 i i i r i i i i i English et al. ------Diehl and Koppany ------Wallis (C=1.0) ...... 4 Wallis (C=0.7) ...... I Pushkina and Sorokin ------

I 3 a 73 2 I a 1

0 J____I___ I____I____L 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

(L/G) Ratio of superficial liquid to vapor mass flow rates

Figure 2.3: Calculated flooding velocity for methane at 10 in a 20 mm (i.d.) tube

English, Jones, Spillers and Orr [34] present an empirical correlation, Equation 2.2. The correlation predicts a maximum superficial vapor mass flow rate (G) at the bottom of the condenser. They state that this mass flow rate depends on tube diameter (D), liquid and vapor density (pv, pi), surface tension (a), liquid viscosity (pi), tube-taper angle ($) and the ratio of liquid and vapor superficial mass flow rates (L/G). This cor relation is based on 56 flooding experiments done by the authors on water, n-propyl alcohol, n-heptane and carbon tetrachloride. The flooding point is taken as the top point of the pressure drop curve in Figure 2.1.

£)0.3p0.46a0.09p0.5 G 1550 (2.2) tf-14{cose)°-32(L/G)0-07

G, z; Superficial vapor and liquid mass flow rate - lb/h ft2 D Tube inner diameter - in. Pli Pv Liquid and vapor density - lb/ft3 <7 Surface tension - dyne/cm Pi Liquid viscosity - cp e Tube taper angle (from horizontal) - degrees

Experimental and Theoretical Study of Reflux Condensation 2.2 Flooding point prediction 11

Diehl & Koppany [33] also present an empirical correlation for prediction of the superficial flooding velocity (u„). The authors report that flooding is dependent on a critical diameter determined only by surface tension (a). In addition, the flooding velocity depends on tube diameter (D), vapor density (pv) and the ratio of liquid and vapor superficial mass flow rates (L/G). This correlation is based both on experiments by the authors (hydrogen-diesel oil, water, and steam-air-water) and on measurements done by others. The flooding point is defined (unclearly): “ The flooding point was determined in the tests by noting the velocity at which a large increase of entrain ment occurred and by checking the pressure drop increase as the vapor velocity was increased.”

F\F2 (2.3)

D ' Fi < 1.0 <7/80, ' D Fx 1.0 > 1.0 .<7/80 F2

uv Superficial flooding velocity of vapor - ft/s fi, # Correction factors o Surface tension - dyne/cm

Pv Vapor density - lb/ft3 D Tube inner diameter - in. Z, G Superficial liquid and vapor mass flow rate - lb/h ft2

The correlation given by Wallis [35], Equation 2.4, is probably the most commonly used for prediction of the flooding point. This equation is referred to as semi- empirical. The flooding point predictions are made on the basis of water-air experi ments. The sum of the square root of the liquid and vapor dimensionless velocities (p,j„) is predicted to be constant at the flooding point. The equation is valid for tubes and packed columns. The constant (C) varies with geometry of the tube or column.

Experimental and Theoretical Study of Reflux Condensation 12 2 LITERATURE REVIEW

# +;7 = c (2.4) Gy,in jv — VPv (Pi ~ Pv) 9 Dh Gj7 in 31 = y/Pi (pi ~ Pv) 9 Dh

Jv Dimensionless superficial vapor velocity 31 Dimensionless superficial liquid velocity C Constant (0.7 - 1.0) G.vjini It u Superficial vapor and liquid mass flux at inlet - kg/m 2 s Pvt Pi Vapor and liquid density - kg/m 3 9 Acceleration due to gravity - m/s2 Dh Hydraulic diameter - m

Pushkina and Sorokin [36] found that tube diameter is invariant in the interval between 6 and 309 mm. They recommend the Kutadeladze correlation, Equation 2.5, which is based on water-air experiments. Flooding is predicted as the vapor velocity (uy ) where flow reversal occurs and is claimed to depend on surface tension (a), vapor and liquid density (pv,pi) and the acceleration of gravity (g).

gv{pi - Pv) 0.25 uv 3.2 (2.5) Pv2

Viy Flooding velocity of vapor - m/s 9 Acceleration due to gravity - m/s2 a Surface tension - N/m Ph Pv Liquid and vapor density - kg/m 3

Both Equation 2.2 and 2.3 are dimensional, and take English engineering units as in put in the listed form. The equations must therefore be carefully converted to comply

Experimental and Theoretical Study of Reflux Condensation 2.3 Processes utilising dephlegmator technology 13 with SI units. This was done when comparing the different equations. Girard & Chang [37] have recently developed an elaborate system of equations that treats wave stability in order to solve the flooding problem. Even with a set of eight simplifying assumptions, their model is rather complex. The model is verified by experimental data obtained in 4.8 m long Pyrex tubes of 2.06,1.59 and 0.95 cm i.d. The work is done with focus on water cooling of fuel rods in nuclear power plants, and does not consider mixtures. For tube bundles some authors recommend a reduction in velocity of between 30% and 50% of the flooding correlations [18,29], The discrepancies in existing theory and experimental work do not lead to any strong conclusions. The flooding correlations have generally been developed for circular tubes with large diameters (typically 3/4 inch). The geometry of the actual equipment should always be checked against the experimental setup that was used to develop the different correlations. Limb & Czamecki [38] have tested different flooding correlations in plate-fin chan nels. The authors state: “These data confirm that most of the existing correlations are suspect for equivalent diameters below 3/4 in., with the possible exception of the Wallis correlation. ’’ The present work focuses both on rectangular plate-fin channels and circular tubes. The Wallis correlation is, supported by the above statements, used throughout this thesis.

2.3 Processes utilising dephlegmator technology

The literature on process integration with dephlegmator technology is dominated by articles and patents from Air Products & Chemicals Inc. (APCI). Ethylene recovery has been their main concern, but various combinations of gas separation are suggested and patented [2,3,39,40], The literature from APCI includes several patents (listed in Appendix A). Connected processes such as recovery from synthesis gas, COg, N2, He, HgS and H2 recovery are also presented [38-41]. Some industrial experience with dephlegmator technology is reported, and examples are reproduced below. Absorption refrigeration cycles with H2O-NH3 or Li-Br refrigerant is a field where dephlegmator technology gains some attention [2,3]. Various older patents, mainly from the 1920s and 1930s, describe distillation and

Experimental and Theoretical Study of Reflux Condensation 14 2 LITERATURE REVIEW cracking of valuable gases from coal shales, solids and oils [2,3]. Utilization of these processes are believed to have been hampered by development of other more suitable processes. Recovery of hydrocarbons from fluid catalytic cracker off-gas using dephlegmator technology is a feasible process [41]. The introduction of dephlegmators in the cryo genic section reduces refrigeration duty significantly. Expanded top product from the dephlegmators may be sufficient to cover the condensing duty. Brahn [41] reports satisfactory economy for such plants, i.e. significant cost reduction and pay-back time less than two years. A similar process for recovery of NGL from natural and associated gases is reported by Limb & Czamecki [38,42] with several alleged advantages. By replacing a turbo expander process with a high pressure process (with dephlegmators), better turn-down capability and power savings of 40% are reported. An installation at the Kincora gas terminal in Australia is reported to work better than design (95% propane recov ery). The authors briefly present some new applications for the process, of which one is hydrocarbon dew point control. The reflux heat exchanger will separate out heavy components at higher temperatures and save about half the refrigeration duty according to the authors. Limb & Czamecki also indicate applications such as ethane recovery, dual mode plant4, supercritical feed and LNG production.

A thermodynamic analysis of separation in refineries and natural gas handling is given by Rojey [43]. Distillation with heat exchange is given attention, and a process is presented where the rectifier of a distillation column is replaced by a dephlegma tor. Optimization is done with focus on reducing necessary equipment, temperature difference and entropy production. This leads to reduction in both investments and op erational costs. For propane-butane separation, 99% recovery of propane is achieved with increased refrigeration temperature from -85°C to -60°C. A 30% reduction in refrigeration duty is reported. IMI Marston, a manufacturer of plate-fin heat exchangers, identifies a number of processes in which PFHE dephlegmators are suitable. These are: extracting helium from natural gas, condensing argon, hydrogen purification, COg purification, ethylene recovery, ammonia purge gas separation, etc [44]. ALTEC, another PFHE manufac turer, also promotes reflux condensers for applications such as air separation, refinery & petrochemical recoveries, natural gas processing and refrigeration systems [45].

4The suggested dual mode plant handles both ethane and propane recovery

Experimental and Theoretical Study of Reflux Condensation 2.3 Processes utilising dephlegmator technology 15

The term dephlegmation is used in membrane separation technology [46] for adia batic separation in membranes. This technology is not considered to be a part of the subjects covered by this work.

Experimental and Theoretical Study of Reflux Condensation 16 2 LITERATURE REVIEW

Experimental and Theoretical Study of Reflux Condensation 3 Theory

Reflux condensation in dephlegmators offers, in principle, some intriguing advantages to both conventional distillation processes and partial condensers. Heat removal at a gliding temperature range is one feature that may improve thermodynamic efficiency. In a conventional distillation column, all heat is removed at the lowest temperature in the condenser. The temperature difference between the condenser and the surround ings may be substantial (cryogenic temperature). The driving forces for mass transfer in a conventional distillation column are often large, especially around the feed point. In a dephlegmator, the driving forces are small, and the irreversible loss due to mass transfer is significantly reduced. The rea son for this is that the reflux flow of liquid enhances stripping of the light component from the liquid phase. Liquid in down-flow is continuously exposed to vapor at a higher temperature, enabling the light component to re-evaporate. In order to fully understand the possibilities and limitations of this technology, the different factors that govern the utilisation of dephlegmators must be investigated. It is important to obtain knowledge about the physical basis of the dephlegmation pro cess, and to identify the more important parameters. This applies to both design and operation of such equipment. In this chapter, the following subjects are discussed:

• Heat- and mass transfer

• Flooding

• Pressure dependence and pressure drop

3.1 Multicomponent heat- and mass transfer

A thermal process device, such as a dephlegmator, which is designed to separate liquid and vapor fractions with binary or multicomponent mixtures, is constrained by the physics of heat- and mass transfer. The significance of the different contributions varies with temperature, pressure, fluid properties, flow rates, geometry and heat flux.

Heat transfer

A temperature difference always leads to heat transfer from the high- to the low tem perature. The rate at which the heat transfer takes place depends on the temperature difference, thermal properties and geometry of the materials involved. Determination

17 18 3 THEORY of heat- and mass transfer coefficients is recognized as a challenge in modeling. The heat transfer coefficient, a, is commonly assumed to vary with flow rate, geometry, mass transfer and properties of the actual fluid mixture. Correlations for these coeffi cients are mainly empirical, and may contain substantial uncertainty. This is indeed true for complex geometries and multi-phase flow. The heat transfer coefficients needed in this text are obtained from open literature and cited where used. Condensation of a multicomponent mixture is a process where both composition 1 and temperature of the liquid and vapor phase change. This is illustrated in Figure 3.1 for a binary mixture. Super-heated vapor is cooled to the dew point (1). Further cooling splits the feed vapor into a two-phase mixture of vapor and liquid. The first condensed liquid (2) is rich in heavy components. Both vapor phase and liquid phase are enriched with light components throughout the two-phase region. This means that both the dew point temperature (1—»3—>5) and the boiling point temperature (2—»4—»6) of the mixture decrease. Total condensation is accomplished in point 6.

Liquid-vapor

Composition (increasing light ) 100%

Figure 3.1: Illustration of the condensing process in a T-x plot (Binary mixture, constant pressure)

‘Composition of a binary mixture refers to the lighter component, if not differently specified, throughout this thesis

Experimental and Theoretical Study of Reflux Condensation 3.2 Flooding 19

Mass transfer

In a gas or liquid mixture with a concentration gradient, mass transport by diffusion may occur. The condensation process illustrated in Figure 3.1 serves as an example of a process where mass transfer develops. When the heavy component is transferred into the liquid phase, the concentration in the vapor is lowered in the vicinity of the vapor-liquid interface. The concentration gradient between the bulk and the interface initiates mass transfer by diffusion. Similarly, the light component diffuses from the interface towards the bulk of the vapor. Pick’s law describes this transport in a binary mixture, Equation 3.2, and states that mass transport by diffusion in a binary mixture is proportional to the concentration gradient.

(3.1) (3.2) (3.3)

The interaction effects in a ternary mixture is treated by Taylor & Krishna [14]. The “three-way ” interaction renders a possibility of diffusive transport with no gradient, known as osmotic diffusion and transport against gradients, reverse diffusion. These phenomena, illustrated in Figure 3.2, occur because transport is dependent on the gradients of the other compounds in the mixture. In a system with macroscopic flow, mass transfer by bulk transport is also present. The total transport of one component is:

Na = Ja + Nt/a (3.4)

For mixtures containing multiple components, the challenge of describing mass trans port becomes complex, and will not be elaborated here.

3.2 Flooding

Flooding in counter-current vertical flow is obtained when a rapid increase in pressure drop is observed with increasing flow rates. An illustration of this is given in Figure 2.1. Vapor friction on the liquid film increases with increasing flow rate, and waves form on the liquid surface. Further increase of vapor flow rate leads to liquid bridging

Experimental and Theoretical Study of Reflux Condensation 20 3 THEORY

Binary diffusion Ternary diffusion

J1 J1 Osmotic diffusion Normal Diffusion \ diffusion behaviour

dxl o dxl

Reverse Normal diffusion diffusion behaviour

Figure 3.2: Mass transfer - diffusion vs. concentration gradient [14] of the flow channel. The flow regimes resulting from further increase in flow rate (especially vapor rate) are complex, and highly statistical in nature, until a reversal to co-current annular flow is obtained at yet higher vapor flow rates. The mechanisms of flooding are treated in detail elsewhere, as reported in Section 2.2, and will not be discussed here.

3.3 Pressure dependence and pressure drop The pressure has a significant influence on a separation process. At high pressure, the two-phase region in Figure 3.1 shrinks. The boiling- and the dew point line shifts upwards, and the temperature difference between them decreases. This is shown in a temperature-composition diagram for methane and ethane in Figure 8.1. At elevated pressure, the temperature needed to liquefy gas increases, while the volatility decreases. High relative volatility eases the separation of gases. The relative volatility of two gases is defined as (component a being the more volatile of the two):

(3.5)

If the relative volatility is greater than unity, separation is possible. aab is temperature and pressure dependent. The above mentioned pressure dependence indicates an optimization task on design of separation equipment, with volatility and separation

Experimental and Theoretical Study of Reflux Condensation 3.3 Pressure dependence and pressure drop 21 efficiency on one side, and refrigeration and compressor duty on the other. The pressure dependency is studied in some detail in Chapter 8, as a part of the case studies with the numerical model. Pressure drop in reflux flow is generally low due the limited flow rates, restricted by flooding, as discussed in Section 3.2. This is supported by the example reported in Figures 3.3 and 3.4 below. The equation for conservation of momentum in two-phase flow [47] is given by Equation 3.6. By assuming a vertical tube2, separate flow of vapor and liquid phase, uniform density in each phase and constant shear stress, the momentum equation is integrated to Equation 3.7. a is the void fraction of vapor phase.

+g[apv + (1 - Oi)pi] (3.7)

The total pressure drop in a two-phase flow may now be classified into three terms due to friction, gravity and acceleration, Equation 3.8. These separate terms are recognized on the right hand side of Equation 3.7. The frictional pressure drop, Equation 3.9, has two terms, one due to friction between wall and liquid, and one due to friction between liquid and vapor. By using friction factors from White [48] for both wall and liquid-vapor interface, the frictional pressure drop is given by Equations 3.9, 3.12, 3.13 and 3.14. Reynolds number and friction factor are calculated for liquid and vapor, respectively, for wall and interface. Pressure drop due to gravity is given by Equation 3.10, and due to acceleration by

^Positive z direction is upwards

Experimental and Theoretical Study of Reflux Condensation 22 3 THEORY

Equation 3.11.

_ W ^ (3.8) dz J acc ) tot \ jz V \ ^ grav

{SWTW + 5/7"/) (3.9) fric

g[apv + (1 - o;)pi] (3.10) grav ^ acc — [o.Gvuv + (1 — a)Giui]

d &G2 + (1 - ol)G2 dz pv pi (Gl_G±\^ , 2<*G vdG v \Pv Pi ) dz pv dz

I o(l ~ a)Gi dGi _ aG2 dpv (1 — a)Gj dpi (3.11) pi dz pi dz Pi dz fG2 (3.12) 8 P 64 flam (3.13) Ee f— 1.8 log 6.9 fturb Ri + (3.14)

uD Re

The different terms of the pressure drop correlation is evaluated below, based on process data from the test rig described in Chapters 5 to 7. The data in Table 3.1 are taken from one of the measurements, named tl00697, in Appendix G. This is the measurement with the highest wall heat flux, separation and reflux ratio. The void fraction is assumed to be 1.0 at the top, and to vary linearly from top to bottom of the tube. The pressure drop, and the single terms in Equation 3.8, are plotted in Figures 3.3 and 3.4 as a function of void fraction. Hewitt [47] reports data for vertical upwards flow with void fractions between 0.9 and 1. This interval is used in the figures. Pressure drop in the tube is in the order of 2 to 5 mbar/m in a dephlegmator tube

Experimental and Theoretical Study of Reflux Condensation 3.3 Pressure dependence and pressure drop 23

(with properties as listed in Table 3.1), at void fractions varying form 0.9 to 1 at the inlet of the tube. The dominating contribution to the overall pressure drop is due to gravity. The relatively low pressure drop validates a constant pressure assumption in the remaining theoretical work in this thesis.

Top Bottom Unit G i 0.00 -17.20 kg/m 2s Gv 13.40 26.50 kg/m 2s Pi 499.80 501.53 kg/m 3 Pv 23.43 23.56 kg/m 3 dGi 8.62 kg/m 3s A dz -6.56 kg/m 3s dpi -0.87 kg/m 4 dpv -0.07 kg/m 4 da 0.15 m_1 L 2.00 m D 21.4 mm p 10.87e5 Pa e 0.0015 mm

Table 3.1: Data for pressure drop calculation (Measurement 1100697)

Experimental and Theoretical Study of Reflux Condensation 24 3 THEORY

Total Gravity

Inlet void fraction (-)

Figure 3.3: Total- and gravitational pressure drop in dephlegmator tube as a function of void fraction

Acceleration 60 - Friction (wall) Friction (interface)

20 -

-20

-40 -

0.9 0.92 0.94 0.96 0.98 Inlet void fraction (-)

Figure 3.4: Pressure drop due to acceleration and friction in dephlegmator tube as a function of void fraction

Experimental and Theoretical Study of Reflux Condensation 4 Numerical model

Several models of reflux condensation are reviewed in Section 2.1. These are based on conservation of species, mass, momentum and energy, in addition to equilibrium at the interface between liquid and vapor. The models tend to involve a large amount of equations to be solved. Insufficient physical models for prediction of properties and heat- and mass transfer coefficients, reduce accuracy. Such a model is dependent on initial values and require iterative solution schemes. Numerical difficulties with complex models have been reported [19]. The various physical effects of a large number of unknown properties are difficult to judge, and the quality of such models as design tools, and the results produced, may be doubtful. This chapter presents a simpler and different approach, in which all simplifications are discussed and the effects of these are surveyable.

4.1 Model basis and assumptions Figure 4.1 displays a control volume of the current model, where the different param eters are named. The system is assumed to be isobaric, an assumption which reduces the number of equations, as the momentum equations are neglected. Pressure drop in a dephlegmator was discussed in Section 3.3. I f

-—

T, c h Tv 9w naj nb (j X |X, q v y :y i

Liquid Interface Vapor °4 -G-t

Figure 4.1: Control volume for reflux condensation model

The conservation equations for mass, species and energy in liquid and vapor phase are listed in Equations 4.1 to 4.8. Diffusion of mass and heat in the axial (flow) direction is neglected in this system. The non-linear differential algebraic system

25 26 4 NUMERICAL MODEL consists of 6+2NOC independent equations and 8+4NOC variables. In order to solve the equations, a set of assumptions and closure laws must be added.

dGv NOC - ni Si = 0 (4.1) dz i=i dGi NOC (4.2) dz + E ni^1 - 0 2 = 1

- Gvyi ) - ni Si = 0 (4.3)

Gi Xi) + rii Si = 0 (4.4) dz NOC — y — Gvhvj —Si(qv+ E^2 nihv,i) — 0 (4.5) 2=1 NOC Gi hi j -f- Si (c[v ^ ] fiihv i qw ) — 0 (4.6) dz i=1 NOC E y* -1 = 0 (4.7) 2 = 1 NOC E Xi - 1 = 0 (4.8) 2 = 1

The system could be solved, simultaneously for the whole dephlegmator, by a dif ferential algebraic equations solver. The main disadvantage of using such a strategy, and the rationale for not using it here, is loss of control with the different variables during the calculations. Proceeding from the conservation equations, the aim was to develop an analytical solution to the problem of reflux condensation. The system is reduced to a binary mixture. This constraint is not strictly necessary, but the binary case is more surveyable than cases with multiple components. An ex tension of the model to handle multicomponent mixtures postponed until a thorough understanding of the binary case is obtained. This assumption reduces the number of conservation equations to eight, four in each phase. A linear interpretation of the remaining differential algebraic equations is needed to

Experimental and Theoretical Study of Reflux Condensation 4.1 Model basis and assumptions 27 obtain an analytical solution. The composition sums and the heat- and mass transfer Equations (4.9 - 4.11) are substituted. The system is reduced to six independent equations.

nb = ^[(1 + y)na +k (yj-y)] (4.9)

qv - av{Tv — Tj) (4.10) qw = ai(Ti-Tw) (4.11)

To close the system of equations and variables, an assumption is made with respect to the liquid phase composition, as the liquid phase is assumed to be saturated. In mass transfer modeling [14], it is common to make a choice between a completely mixed- or an unmixed liquid phase. The effect of the two optional choices is significant at low heat flux. Here, the assumption is made that the liquid phase is well mixed without sub-cooling. This assumption must be kept in mind, and the model should be used with care at low heat flux, and in the presence of non-condensible components. The interface perimeter, 57, is set equal to the tube perimeter in the model. Interface conditions are defined to be saturated at the liquid temperature. This defini tion is formulated in Equations 4.12 - 4.14.

Ti = Ti (4.12) VI = %(T,,Tr* (4.13) XI = c(T;,T)"* (4.14)

The effect of the assumptions are discussed in Section 7.3. A set of linear thermodynamic relations are substituted into the equations. These are necessary in order to obtain a linear system of equally numbered variables and equations. A first order Taylor series expansion of the thermodynamic relations is used. As an example, first order Taylor series expansion of enthalpy in the vicinity of a known point, h(To, To, A7,o)> is shown in Equation 4.15. The second order term, 9 (AT2, AT2, AN?), contains the deviation between the real and the approximated value. By reducing the step length, the alteration in the thermodynamic properties are small. The method is consistent with small steps, as the error in the Taylor

Experimental and Theoretical Study of Reflux Condensation 28 4 NUMERICAL MODEL approximation is reduced in the second order error term1.

(4.15)

The thermodynamic Equations, 4.16 - 4.22, are listed below. When substituting these into the conservation equations, a set of six equations with six unknowns is obtained. The unknowns are: na, £ Gv, ^ Gu £ y, j-z Tv and £ 2).

(4.16)

hi — hliref

(4.19) (4.20)

(4.21)

(4.22)

The solution method is more compact when the variables and equations are denoted as matrices, Equation 4.23. The conservation equations, with substituted linear thermodynamic functions, are shown as matrix elements in Appendix B. The analytic solution is obtained in Equation 4.24. The solution vector, x, was not as simple as desired, as the matrix elements contain multiple terms. The rationale for obtaining an analytical set of equation, is to examine the different parameters effect on the solution. This analysis demands an overview of each variable, which was lost due to

'The error term reduces proportional to the square of the step in each direction (T,P,Ni)

Experimental and Theoretical Study of Reflux Condensation 4.1 Model basis and assumptions 29 the complexity of the analytical solution.

A x = R (4.23) x = A-1 R (4.24)

A - Coefficient matrix (6 by 6) x — Solution vector (6 by 1) R - Residual vector (6 by 1)

The model need initial values for at the start of the calculations. The required initial values are listed in Table 4.1. A numerical solution procedure was chosen, where the equations are solved by a matrix solver using Gauss elimination. The numerical integration is done by a fourth order Runge-Kutta method with variable step size [49]. The model can advance either upwards or downwards, dependent on the specified initial data. The thermodynamic properties are calculated from the initial values, along with heat- and mass transfer coefficients.

Initial value Description y kmole/kmole Light composition of vapor phase Gy kmole/s Molar flow rate of vapor G, kmole/s Molar flow rate of liquid Ty K Vapor phase temperature T, K Liquid phase temperature P Pa Pressure q«? W/m2 Wall heat flux (May also be specified as wall temperature)

Table 4.1: Initial value input to numerical model

Experimental and Theoretical Study of Reflux Condensation 30 4 NUMERICAL MODEL

4.2 Model implementation for an arbitrary heat exchanger

The model is programmed in C, and takes input as specified in Table 4.1 at one end of the dephlegmator. In addition, a criterion is set, at the opposite end, to determine when to stop the numerical integration. This criterion may be chosen between composition, flow rate, length of dephlegmator or flooding point. Thermodynamic properties are calculated using an in-house thermodynamic library, where the Peng-Robinson equation of state [50] is used. Appendix D describes the equation and mixing rules, used on the test mixture of propane and n-butane in the laboratory test rig (Chapters 5 and 6). Flooding is monitored by calculating the Wallis flooding coefficient (Equation 2.4). In a multi-tube heat exchanger, some authors recommend a reduction in flooding factor [18,29]. In this program, the flooding coefficient is printed to the output file, and can be evaluated according to the comments made in Section 2.2. The vapor phase heat transfer coefficient is calculated by Equations 4.25 or 4.26, taken from Kays & Crawford [51]. Nusselt (Nu) number denotes a dimensionless temperature gradient at the surface, and the Prandtl (Pr) number denotes the ratio of the momentum and thermal diffiisivity. There are several equations for pure gas flow in the literature, but no work has been done to evaluate and choose between them in the reflux flow case. The different correlations only differ slightly on constants and exponents. These details are important enough for some applications, but are considered to be of secondary importance here.

Hlam — 4.64 (4.25) N.V'turb ~ 0.023 Re0-8 Pr0-333 (4.26)

a Dh Nu = A u Dk Re = V cpfi Pr = A

When constant wall temperature is specified, the film heat transfer coefficient is calculated from film theory [13].

Experimental and Theoretical Study of Reflux Condensation 4.3 Model implementation for PFHE 31

The the mass transfer coefficient, k, is calculated from Equation 4.27.

(4.27) v MWVXV \cpvpvDabJ

The program can calculate a dephlegmator with arbitrary geometry, and is used in Section 7.2 for the experimental test rig. The calculations in that section form the connection between the experimental study and the theoretical model. By comparing the experimental results and calculation, the quality of the model is evaluated.

4.3 Model implementation for PFHE

...... r ! 5 T h —» t 1 ! -i p i-—

Figure 4.2: Fin geometry of a plate-fin heat exchanger

The model for a plate-fin heat exchanger is a specialised version of the model de scribed previously. The flooding point and heat transfer coefficient are calculated as described in the previous section. The heat transfer coefficients used here are conservative because a rectangular channel has higher heat transfer coefficient in the laminar region than a circular tube. The value depends on the ratio of length to width of the channel, and may be up to 150% of the value in a circular tube (p.43 of [52]). The design of a plate-fin dephlegmator is assumed to be constrained by feed specifica tions, top product requirements and a predefined footprint area for the heat exchanger. Fin geometry and heat exchanger external measures are specified. The program cal culates heat transfer area and required thickness of the fins and separating plates. Fin geometry is displayed in Figure 4.2, and the correlations for characteristic geo metrical data are given in Equations 4.28 - 4.34.

Experimental and Theoretical Study of Reflux Condensation 32 4 NUMERICAL MODEL

tfin — (4.28) in G £ tpi — (4.29) a 0.5 ( P tp 2 = (4.30) P

II (4.31) 2 'fifin'^ glP-Zf Dh = (4.32)

(P — 2 t/m + Si = 4>WH (4.33) (h + tp)p tp tfin P tfin) An = 4>WH[1- (4.34) h + tp (h + tp)p

Where: Dh - Hydraulic diameter P - Fin spacing tp Separating plate thickness h - Fin height Ac Cross flow area S/ - Heat transfer area/m W - Heat exchanger core width tym - Fin thickness H - Heat exchanger core height n/iro - Number of fins/m a Maximum allowed tensile stress b - Half fin height(h/2) r Maximum allowed shear stress P - Pressure tpi - Plate thickness (tensile stress) 0 - Area factor tp2 Plate thickness (flexural stress) tp3 Plate thickness (shear stress)

The area factor, , introduced in Equations 4.33 and 4.34, is included to calculate the actual area occupied by dephlegmator channels. The heat transfer area per core length, Si, is estimated with the assumption that 25% of the available core geometry is used for coolant. This assumption, with (j> = 0.75, is made because the coolant side is not restricted by flooding and can be designed with smaller channels. This leads to higher area to volume ratio on the coolant side and more available space for extra reflux channels; thus giving more heat transfer area per length. The value of the

Experimental and Theoretical Study of Reflux Condensation 4.3 Model implementation for PFHE 33

area factor depends on the chosen cold stream in the design process. Several process streams may be used for cooling duty, but the coolant side is not explicitly treated in the current model. Flow and pressure distribution, and instability due to these effects, are not calculated by the model.

Preliminary design

Mechanical design of plate- and fin thickness is possible regardless of process fluids, as pressure govern the design of plate- and fin thickness inside a PFHE unit. Fin and plate thickness are calculated by Equations 4.28 - 4.31 based on design pressure and fin geometry. The plate thickness is taken as the maximum2 of tpi, tp2 and tp3 . Minimum fin thickness is 0.15 mm and minimum plate thickness is 0.8 mm. Data from these calculations are used to calculate hydraulic diameter, heat transfer area and flow area by Equations 4.32 - 4.34. The design task is, in essence, optimization between heat transfer area and flooding. High density of heat transfer area is desirable to minimise the overall dimensions of the unit. Flooding factor below a limiting value is necessary to operate the dephlegmator as a reflux flow device. Heat transfer area per meter is calculated by Equation 4.33. The flooding factor (Equation 2.4) is inversely proportional to the square root of the flow area multiplied by the quadratic root of the hydraulic diameter, C ^0.5— FR.

For a design pressure of 40 bar and core 3 width(W)/height(H) of 1.2 m, the area variation and flooding ratio (FR) are displayed in Figures 4.3 and 4.4 for different combinations of fin spacing(p) and height(h). The effect of fin spacing is contrary for the two criteria. Small fin spacing is desirable to obtain high area, high fin spacing is desirable to obtain low flooding factor. The last statement being valid for fin heights above approximately 3 mm, thus fin height greater than 3 mm is reasonable in order to avoid flooding. The heat transfer area is dependent on fin spacing, while the flooding ratio only varies slightly (h > 3mm). The significant decrease in heat transfer area with increasing fin spacing leads to the conclusion that fin spacing should be minimised in each case, subject to the flooding limit. Fin spacing less than 1 mm is not common

^Maximum allowable tensile stress for aluminium is taken as 23 MPa, and maximum allowable shear stress is half this value ^Maximum available stacking height and width are commonly about 1.2 m

Experimental and Theoretical Study of Reflux Condensation 34 4 NUMERICAL MODEL among commercially available plate-fin heat exchangers.

Heat transfer area variation

1800 - p = 1 mm p= 2mm 1600 - p = 3 mm p = 5 mm 1400 -

P = 40.0 bar

Fin height - h (mm)

Figure 4.3: Sensitivity of PFHE heat transfer area to variation of fin geometry

The non-linearities observed in Figures 4.3 and 4.4 are due to the different design plate and fin thickness with changing fin heights and spacing. The final choice of geometry is left to the engineer, and focus should be set on maximizing fin pitch (minimising fin spacing). In the following case studies(Chapter 8), separate fin geometry is chosen for each case. Sensitivity analysis is performed on these data.

Experimental and Theoretical Study of Reflux Condensation 43 Model implementation for PFHE 35

Flooding ratio variation

= 40.0 bar

Fin height - h (mm)

Figure 4.4: Sensitivity of PFHE flooding ratio to variation of fin geometry

Experimental and Theoretical Study of Reflux Condensation 36 4 NUMERICAL MODEL

Design procedure

A general procedure for design of plate-fin dephlegmators is outlined here. The input is assumed to be feed properties, top product composition and pressure. The design should comply with limitations given by manufacturers of plate-fin heat exchangers. Some typical values are given in Table 4.2 for aluminium units. The procedure is used in Chapter 8.

Item Maximum Minimum Unit

Pressure P 80 - bar

Width W 1200 - mm Height H 1200 - mm Length L 6200 - mm Fin width P 5 1 mm Fin pitch 1000 200 fins/m Fin height h 12 3 mm

Table 4.2: Plate-fin dephlegmator design - parameter range

(D Specify input: Feed flow rate(F), feed composition^jeed), top product composition(y top ). Specify operational pressure(P). If not specified by process, the pressure may be chosen. Low pressure enhances separation, high pressure increases coolant temperature.

® Initial value: Study a T-x diagram of the actual mixture, and calculate top and reflux flow rate from approximated composition of the liquid reflux. This is used as an initial value. Set heat flux.

(D Core external geometry: Set W and H to maximum allowable. In case of predefined footprint area, the values are given. If not specified, use maximum from heat exchanger manufacturers (1.2m).

Experimental and Theoretical Study of Reflux Condensation 4.4 Comparison with other models 37

© Execution: Run program © Flooding limit: To enhance heat- and mass transfer, the unit should be operated close to, but not above the flooding limit. • If flooding limit is not exceeded, reduce h and return to ©. p and h may be varied in the following intervals: p = [1..5] mm, h = [3..12] mm. If reduction of p and h is not sufficient, reduce W and H. Return to ®. • If flooding limit is exceeded, increase p and h. Return to ®. If flooding factor is still to high with maximum p and h, more than one dephlegmator is needed. Divide feed flow rate into smaller fractions and return to @. Calculate one unit at the time. © Core length: If L exceeds maximum allowable (Either decided by space restrictions or man ufacturing limitations (6m)), increase heat flux. Return to ®. ® Bottom product quality: If a specified quality of the liquid reflux is required, the heat flux must be varied. Return to ©. © Pressure design: If pressure is subject to design, vary pressure and return to ©. © Completion: Design is complete.

4.4 Comparison with other models An attempt was made to compare the model with results in published literature. It is impossible to establish rigid comparison schemes due to insufficient information or detailing level in the various publications. The lack of publications is also pointed out by Davis et al. [19]. Di Cave et al. [21] studies a single tube dephlegmator. Insufficient information on flow rates and heat duty, unfortunately makes comparison difficult. Only flow rate ratios in the condensing section are reported in addition to inlet temperature and flow rate of the coolant. The flow rate ratios supplied are condensing ratio and reflux ratio. 15 experiments are reported 4, of which three are compared here.

4The 15 experiments are divided into three groups with similar properties

Experimental and Theoretical Study of Reflux Condensation 38 4 NUMERICAL MODEL

Figure 4.5 displays a comparison with experimental runs for a n-hexane/n-octane binary mixture. The data points refer to experiments 3C, 5D and 4E in Reference 21. The assumptions made (by this author) are constant wall temperature and atmospheric pressure. The wall temperature is set equal to the coolant temperature for each of three runs. The agreement, as shown in the figure, is good.

l i i i i i i x Condensation ratio 0.9 y_b x_b 0.8 ; X: 46 3 °'7 X - i °-5 -X g 0.4 5 0.3 : X' "

0.2 -

0.1 0 . . — -1_____1_____1____ » —1_____1____ 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Experimental value (-)

Figure 4.5: Comparison between model results and data from Di Cave et al. [21] - condensation ratio and composition

Experimental and Theoretical Study of Reflux Condensation 5 Test facility

Literature describes experimental work on reflux condensation as stated in Chapter 2. Many articles are dedicated to flooding. Some authors report experimental work on heat- and mass transfer, but the majority treat theoretical development. This section describes the experimental set up for the current project. The plant was designed to demonstrate the dephlegmation principle. To avoid hydrodynamic problems such as unequal pressure drop between channels and distribution of fluid, only a single tube is currently used. The test rig is located in the laboratory at The Department of Refrigeration and Air Conditioning at NTNU. The site is equipped with safety arrangements to handle nat ural gas. Gas detectors identify possible leakage. Safety- and relief valves are vented to the outside of the laboratory building. The staff at the laboratory has experience with several other test facilities containing light hydrocarbons.

5.1 Design Information about design of dephlegmators is scarce, and much of the design work is based upon experience on similar equipment. Although a forced circulation circuit (compressor or blower) poses freedom in operation, a self-circulation system was chosen to keep the system as simple as possible. The test plant, shown in Figure 5.1, consists of three main parts, a test section, a boiler and an overhead condenser. Design pressure is 30 bar and maximum temperature 1 is 80 °C. The rig was tested to 33 bar (gauge) pressure with nitrogen. The operational pressure in the current project was 9-12 bar.

Test section

Dimensions of the test section were calculated on basis of the Wallis flooding corre lation, as described in Section 2.2, and the dimensions of available flow measuring instruments. The test section, Figure 5.3, consists of a copper tube with an outer diameter2of 25.4

‘The maximum temperature is due to limitations in the sight glasses. If these are replaced by bolts, temperature can be increased 2Tube diameters are referred to as outer diameter, if not indicated otherwise

39 40 5 TEST FACILITY

Top product

Condenser

Bottom- product ■

Boiler

Figure 5.1: Dephlegmator test rig [53]

1 - Test section 7 Cooling circuit (test section) 2 - Boiler 8 Cooling circuit (overhead condenser) 3 - Condenser 9 Pressure transmitter 4 - Reflux liquid flow meter 10 Differential pressure transmitter 5 - Return liquid flow meter 11 Heating cables 6 - Bypass vapor flow meter

Experimental and Theoretical Study of Reflux Condensation 5.1 Design 41 mm (21.4 mm i.d.). The test section inner tube is covered by a 38.1 mm diameter cooling jacket, made of stainless steel and divided into four sections. This sectioning of cooling capacity ensures freedom in operation, as both length of cooling section and heat flux may be varied. Cooling duty is supplied by water. Inlet of vapor from boiler and outlet of condensed liquid at the bottom of the test section is done through a specially designed inlet section. As inlet conditions often control flooding in the tube [29,30], this section is flanged and easy to replace.

Boiler

The boiler, Figure 5.4, is a 129 mm stainless steel cylinder. Three individually con trolled 8m (length) - 3mm (diameter) Thermocoax heating elements supply heating. These enter and exit the boiler through the bottom end and are coiled, as shown in Figure 5.5. Maximum total duty is 6 kW. Safety is maintained by level-, pressure- and temperature guards, and a separate safety valve (30 bar). The boiler was pressure tested to 33 bar with water and nitrogen.

Overhead condenser

Vapor from the top of the test section is condensed before flow rate is measured and the liquid is returned to the boiler. The overhead condenser is a water cooled shell and tube heat exchanger (TEMA type E). A modification of the liquid outlet was necessary to ensure low pressure drop through the unit. The outlet is taken directly at the bottom of the condenser shell.

Power supply unit

A separate rack contains power supply and security switches. Heating duty to boiler is controlled separately to each heating element, and total duty is measured. The power supply unit also contains emergency stop switch, pressure, temperature and level switches for the boiler. The connector sheet is shown in Figure 5.2.

Piping, valves and connections

The connecting tubes are in stainless steel, 19.05 mm for vapor flow and 10 mm for liquid flow.

Experimental and Theoretical Study of Reflux Condensation 42 5 TEST FACILITY

Figure 5.2: Connector sheet for power supply unit [54]

Cooling circuits

Both the test section and the overhead condenser are cooled by water. The water is filtered, to avoid fouling. Flow rate and temperature are measured. Heating, in temperature controlled baths, is supplied to both cooling circuits to control the inlet temperature of the cooling water.

Insulation

The test rig is insulated with 10 and 20mm insulation The insulation reduce heat loss and stabilise operation with respect to varying surrounding temperature.

Experimental and Theoretical Study of Reflux Condensation 5.1 Design 43

Cooling inlet — 166.7 mm 0 38.1 mm 166.7 mm 0 25.4 mm

333.3 mm

166.7 mm

333.3 mm

166.7 mm

test, 1/4 266.7 mm

Cooling outlet — L 2000 mm

Figure 5.3: Details of test rig - test section

Experimental and Theoretical Study of Reflux Condensation 44 5 TEST FACILITY

1/4" NPT 1/2" NPT 21.5

bottom

Tube 129x2

T'pipe thread

Socket for level gauge

Detail of socket for level gauge, seen 90 ' angel

1/16" In

!_ -L _

1/4" NPT

Cross section A-A

Figure 5.4: Details of test rig - boiler [53]

Experimental and Theoretical Study of Reflux Condensation 5.1 Design 45

o mo J2C

o as

1/16" NPTF

Heaterlength = approx. 8m

1/16" NPTF "I"

1/4" NPT

Figure 5.5: Details of test rig - heating cable layout in boiler [53]

Experimental and Theoretical Study of Reflux Condensation 46 5 TEST FACILITY

5.2 Instrumentation

There are five different groups of measurements on the test rig. These are measurement of temperature, pressure, flow rate, boiler duty and composition. Instrumentation collects data for interpretation of the process. The process data is also necessary for operation of the test rig. The different points of measurements are shown in Figure 5.1. Data from the different instruments are sampled by a Keithley 2001 multi-meter and Keithley 7001 logger unit. The raw data are collected in a PC and treated separately by a data analysis routine, described in Section 6.3.

Temperaturf measurements

Temperature measurements are conducted by various thermocouples. The test section is equipped with ten 0.5 mm chrome-alumel thermocouples, type E, positioned along the height of the tube, Figure 5.3. The thermocouples are soldered into machined slots in the tube walls. The temperature of the process fluid and cooling water is measured with type T copper-constantan thermocouples, positioned according to Figure 5.1. These are in serted in capillary tubes mounted in the various flow channels. A total of 23 different temperature measurements are performed. The thermal refer ence is water at the triple point. The connections to the thermal reference are shown in Figure 5.6. The thermocouples have been calibrated by regression of temperature to a refer ence thermometer. The reference thermometer is calibrated according to the ITS90- standard by the Laboratory for National Norms in Norway. Accuracy 3 of the type E thermocouples after calibration is ±0.05°C. Accuracy of the type T thermocouples after calibration is ±0.02° C.

Pressure measurements - absolute and differential

Absolute pressure and differential pressure difference over the test section are mea sured by Honeywell ST3000 pressure transmitters. The pressure transmitter was calibrated between 100 and 2500 kPa with an accuracy of ±0.1% of measured value.

3The total accuracy of each measurement is treated in Appendix E

Experimental and Theoretical Study of Reflux Condensation 5.2 Instrumentation 47

• Temperature measuring point ------Cupper ------Constantan o Reference temperature point ...... Chrome ...... Alumel

Ice I

Thermocouple (type T) Thermocoax (type E)

Figure 5.6: Temperature reference connection

The differential pressure transmitter was calibrated between 0 and 500 Pa with an accuracy of ±5% of measured value.

Flow rate measurements

Oval wheel flow meters, Bopp & Reuther type 0106 Agl9 R7/A4, measure volume flow of the liquid from the test section and from the condenser, positions 4 and 5 in Figure 5.1. The uncertainty in volume flow depends on viscosity and flow rate. The supplier claims an uncertainty according to Table 5.1 for a liquid with viscosity=0.3 mPa s.

Flow rate [1/h] Uncertainty 50-160 ± 0.5 % 40-50 ± 0.7 % 25-40 ± 1.5 % 10-25 ± 2.0 %

Table 5.1: Accuracy of instrument Bopp & Reuther type OI 06Agl9 R7/A4

In Table 5.1, the operating range of the volume flow meters is limited downwards

Experimental and Theoretical Study of Reflux Condensation 48 5 TEST FACILITY to 10 1/h. The operation of the test rig has shown that it is necessary to operate the reflux liquid flow meter at flow rates around, and below this limit. An on-site check of this flow meter was therefore conducted. The test section was operated as a total condenser, while the rest of the rig was closed off by valves. The measured flow rate was compared with a calculated flow rate (from conservation equations). The deviation between calculated and measured flow rate is shown in Figure 5.7. The calculated values are higher than the measured values, varying up to 4.5% of the measured value. The calculated deviation agrees with Table 5,1 for flow rates above 101/h.

Measured flow rate (1/h)

Figure 5.7: On-site check of reflux volume flow meter

The bypass vapor flow is measured by a EG&G FT-series turbine flow meter. The flow meter was calibrated with air at the conditions listed in Table 5.2. The producer claims a repeatability of ±0.1 % (based on normal 10:1 range) and a linearity of ±4% of full scale. The bypass flow meter readings are corrected for variations in pressure and temperature. The cooling duty water flow rate to the test section is measured by an Aquametro (VZTH2-8H) impeller flow meter with nominal flow rate 75 1/h and maximum flow rate 150 1/h. This measuring instrument has an accuracy of ±5%. The condenser

Experimental and Theoretical Study of Reflux Condensation 5.2 Instrumentation 49

Calibration 1 Calibration 2 Unit Measure Measure Pressure 29.06 bar 56.30 bar Flow rate range 0.136- 1.797 m3/h 0.137- 1.850 m3/h Temperature range 15.4 - 16.7 °C 14.1 - 17.0 °C Fluid viscosity 5.01-10"7 m2/s 2.56- lO"7 m2/s Fluid density 35.99 kg/m 3 69.92 kg/m 3

Table 5.2: Calibration of instrument EG&G type FT2-8WFR2-PEH1 duty water flow rate is measured by an Aquametro piston flow meter which was calibrated for flow rates between 60 1/h and 6001/h. The accuracy of this water flow measurement unit is ±2% of the measured value after calibration.

Boiler duty measurement The boiler duty is measured by an Electrocontrol energy V1PD3 3-phase energy meter. The instrument was calibrated with a FLUKE multi-meter in the operating range of the heating cables.The accuracy of the boiler duty measurements is 0.3% of the reading plus 0.3% of the full scale.

Composition measurements A gas chromatograph (GC), Hewlett-Packard - HP 5890A, measures the composition of the different streams in the test facility. The GC consists of 3 columns and a thermal conductivity detector. The vapor and liquid sample ports are displayed in Figure 5.1. The liquid sample is evaporated in a boiler before sampling. Samples are extracted from the test rig when stable operation is established. The composition measurements are described in detail in Appendix C.

Experimental and Theoretical Study of Reflux Condensation 50 5 TEST FACILITY

Experimental and Theoretical Study of Reflux Condensation 6 Experimental procedure

6.1 Selection of test fluid

Design of the test facility allows a maximum temperature of 80°C, a minimum cooling water temperature of 5°C, and a maximum pressure of 30 bar (Section 5.1). These values act as limits for operation of the test rig. Selection of test fluids is done with respect to relative volatility, pressure and boiling point temperature. Hydrocarbons are used as test fluids, to obtain measurements on realistic mixtures found in processes in the petroleum and petrochemical industries. Volume fraction of vapor in the boiler is the more significant operational constraint. To ensure safe operation of the heat coil, a level switch is situated above the coil bundle, Figure 5.4. This limits the vapor volume fraction upwards to 0.25 m^/mfot . The limit includes vapor volume in tubes and top condenser. A binary mixture is chosen as test fluid, due to the relative simplicity of calculating thermodynamic properties. Measurements on this binary mixture are compared di rectly to calculations performed with the numerical model, which also uses binary mixtures. Minimum boiling point temperature of the mixture is the boiling point temperature of pure light component at a given pressure. The test rig is currently cooled by water, and the minimum boiling point temperature must be chosen above the water temper ature available. Water supply is maintained at constant flow rate from an overhead tank in the laboratory. Figure 6.1 displays boiling point temperature of some pure hydrocarbons as a function of pressure. The upper and lower temperature limits of the test rig are also displayed. Ethane is clearly not appropriate at pressures below 27 bar. Propane is suitable at pressure above 5.5 bar, and is chosen as the light component. The heavy component should have a high boiling point to ensure high relative volatil ity, but not above the maximum operating temperature of 80°C. If the boiling point temperature is above the upper temperature limit of the test rig, the choice in mixture compositions is limited. Normal-butane fits these requirements, and is chosen as the second component. The vapor composition evaporated from a given binary liquid mixture varies only slightly with pressure. Two different mixtures are used to obtain variation in feed composition to the test section. The fluid mixture in the test rig is weighed as listed in Table 6.1, using an electronic weight with a precision of ±0.001 kg.

51 52 6 EXPERIMENTAL PROCEDURE

Condenser temperature N-pentane Maximum temperature I-pentane -

Propane

300 - Ethane

Pressure (bar)

Figure 6.1: Boiling-point vs. pressure diagram for light hydrocarbons Ci —>C5

The test rig is flushed with nitrogen and evacuated before the test fluid is introduced.

Propane N-butane Mixture Mc3 Nc, xc3 Mn_c4 Nn-C4 xn—C4 [kg] [kmole] [-] [kg] [kmole] [-1 a 2.14 4.85e-2 0.50 2.80 4.82e-2 0.50 b 2.88 6.54e-2 0.60 58.12 4.36e-2 0.40

Table 6.1: Test rig fluid mixture composition

Experimental and Theoretical Study of Reflux Condensation 6.2 Operation 53

6.2 Operation

Based on monitored on-line data, the test-rig is operated at steady-state, when equilib rium between heat supply and heat removal is obtained. The lower design flow rate of the liquid flow meters (101/h) and the flooding point are the main limiting restrictions on operation. Liquid flow rate is mastered by interaction of boiler duty, and cooling duty on both test section and condenser. Flooding is controlled by monitoring the pressure drop over the test section, and by observations through the sight glass at the top of the test section. The different control utilities of the rig are listed in Table 6.2. Both flow rate and temperature of the refrigerant affect the heat flux across the test section tube wall.

Type of control Description Heat supply (Variac) Continuous power supply (0 - 6000 W) Condenser valve (Needle valve) Flow rate of cooling water to condenser Test section valve (Needle valve) Flow rate of cooling water to test section Condenser heater (Heated bath) Temperature of water to condenser Test section heater (Heated bath) Temperature of water to test section Bypass valve (Needle valve) Flow rate in bypass line Top valve (Ball valve) Pressure drop across test section

Table 6.2: Control utilities on test rig

6.3 Data collection and conversion

Data from measurements on the test rig is collected by an on-line data logger. In ad dition, flow rate of condenser cooling water and composition are measured manually. The different measurement points are displayed in Table F.2 in Appendix F. A data analysis routine calculates heat flux, separation, heat loss and temperature profiles. The program also writes an input file to the numerical model. Every data series contain an interval of independent measurements, collected by the on-line logger, for each measurement point. Over a time period with stable signals, a number of individual measurements are collected. The measurement value of each point is taken as the mean value of the signals in the measurement interval. The measurements are evaluated and reported with uncertainty (within a 95% confidence level). Uncertainty analysis is performed in Appendix E.

Experimental and Theoretical Study of Reflux Condensation 54 6 EXPERIMENTAL PROCEDURE

Some of the data developed by the data analysis program are not directly measured, but calculated indirectly based on other measured data. Appendix F describes how data is developed from indirect measurements. The results from the numerical model are compared with the measurement data of every test run, and presented in Chapter 7. Figure 6.2 displays the flow of data for each measurement series.

...1 Calibration data

Manual data Data analysis program ■I Thermodynamic package!

| Numerical input file!

( Numerical model )«.

Numerical results 11 Experimental results

Comparison -—

Figure 6.2: Flow of information in data analysis and model evaluation

6.4 Parameter estimation

The collected data in each measurement series does not necessarily satisfy the con servation equations. This is due to measurement errors, a problem which may be approached in different ways. Individual interpretation of data, based on experience or tradition, is common procedure. As experience differs, this may lead to diverging conclusions on the same data set. A simple presentation of a measurement is to report the raw data individually. This method leaves the interpretation to the reader. The approach is objective, but may not reveal useful information related to the process subject to investigation. Individual measurements may be corrected to satisfy the conservation equations. The

Experimental and Theoretical Study of Reflux Condensation 6.4 Parameter estimation 55 correction is based on calibration or experience. A risk of misinterpretation is present. If there are parallel measurements, data with poor accuracy may be disregarded. Some of the process parameters may also be determined from the conservation equations, giving zero residuals, but not necessarily the correct values. The uncertainty in each measurement may be exploited by statistical methods to ob tain a set of estimated parameters. Parameter estimation is adopted here. A variation in statistical uncertainty between different groups of measurements is ev ident from the collected data. This is listed for each measurement series in Appendix G. The flow rate measurements are particularly susceptible to statistical uncertainty, an observation that is discussed further in Chapter 7. MacDonald & Howat [55] describes a method for interpretation of measured data, where data reconciliation techniques are extended to estimate process parameters. The data reconciliation method is called "maximum-likelihood ” estimation, where a defined statistical uncertainty for each parameter is used to estimate the most likely distribution of the data. The mathematical definition of the method is, to minimise the weighted sum of squares adjustment to the data, Equation 6.1, while satisfying a set of constraints, Equation 6.2. The mathematical method requires normal distribution of the random errors. The distribution of the measured data are discussed in Appendix E. Parameter estimation, by data reconciliation, does not account for systematic errors. Consistent definitions of the residual functions, and the estimate for standard deviation of each variable are necessary.

^ (Zo - Z)? Minimise (6.1)

f(Z) = 0 (6.2)

Z0 - Vector of initial values z - Vector of “true” values n — Number of parameters in Z a - Standard deviation F{ Z) - Set of constraints

Experimental and Theoretical Study of Reflux Condensation 56 6 EXPERIMENTAL PROCEDURE

z7 = [F,V,L,R,B,Tf,Tv ,Tl,Tr ,

Z; Vi 2-1 %R] Qboilt Qcondi Qtesti Qlossi P\ (6.3) Ft L + R-(F + B) = 0 (6.4) Fi Lx + Rxr — (F + B)z = 0 (6.5) f3 Lhi + RIir - (F + B)hp +

The single values in the data vector Z are estimated based on the initial values in Zo, and the standard deviation of the actual measurement, 0{. The estimated set of parameters, Z, is adopted as the true measurement data. The standard deviation of each data value is determined from the statistical uncertainty in the measurement, as listed in Appendix G. The initial estimates for composition, heat loss and feed- and top product flow rate are not based on direct measurements, and an estimate for standard deviation is required. For the composition values, a standard deviation of one mole percent is set. The standard deviation in feed flow rate and top product flow rate are estimated as RMS values of the standard deviations in the remaining flow rates. Similarly, the standard deviation of the heat loss term is estimated as a RMS value of the standard deviation in the remaining energy terms. The deviation between measured(or predicted) and estimated values are shown in Figure 6.3. Labels on the x-axis refer to the variables in the measurement vector (Z). The uncertainty of the reflux flow rate measurement is particularly high, as commented previously in this chapter. This is recognized by a large relative adjustment of the parameter in Figure 6.3. The remaining flow rates are also adjusted significantly due to their high statistical uncertainty. Estimates for temperature, pressure, composition and duty are subjects to minor adjustments. The high uncertainty in the manually measured condenser duty is reflected by the adjustments in this parameter. The measurement results are presented in Chapter 7 and in Appendix G. The first table of the individual measurement data in Appendix G reports raw data, with the accompanying statistical uncertainty, while the second reports maximum-likelihood values. In Chapter 7, the maximum-likelihood estimates are used.

Experimental and Theoretical Study of Reflux Condensation 6.4 Experimental

Parameter and

Theoretical Parameter correction (%) 100 -20 40 60 20 80

estimation 0 Figure

Study * * Q F of

VL 6.3: 1 A S A % □ X

Condensation

Parameter X • i O $ RB

TFTVTLTRz

estimation ..

jjj.. y

of x

measured xRqbqcqtqlP b040897 b010897 b b050897 al50797 b bl al l al30897 C120897 a050897 a al30697 al20697 t 190697 180697 170697 100697

10697 10697 a ?

data A e V V 0 □ X X + • ♦ ▲ • ■ --- 57 58 6 EXPERIMENTAL PROCEDURE

Experimental and Theoretical Study of Reflux Condensation 7 Results

This chapter presents the experimental results obtained from the test rig. Separation of a feed vapor stream into a lighter top product and a heavier reflux liquid is demon strated. The data is first presented independently. Further, the experimental results are compared with calculations performed by the numerical model.

7.1 Experimental results

15 experiments are presented with variations on operating conditions as shown in Table 7.1. A summary of the experiment details is listed in Appendix G, along with output from the data analysis program for each measurement.

Parameter Range Pressure 9.03 12.17 bar Wall heat flux 1682.7 4782.2 W/m2K Feed temperature 46.27 60.28 °C Feed composition (propane) 0.62 0.77 kmole/kmole Feed flow rate 1.18e-4 1.79e-4 kmole/s Top product temperature 42.44 56.38 °C Top product composition (propane) 0.68 0.79 kmole/kmole Top product flow rate 8.84e-5 1.66e-4 kmole/s Reflux liquid temperature 45.26 59.42 °C Reflux liquid composition (propane) 0.42 0.56 kmole/kmole Reflux liquid flow rate 1.24e-5 3.61e-5 kmole/s

Table 7.1: Operating range of test rig

Separation of the feed stream into top product, as a function of wall heat flux is plotted in Figure 7.1. A linear trendline is included to indicate the effect of heat flux. The top product stream is enriched in the light component, varying from 1.7 to 7.8 mole percent. Separation of top product (y-z) increases with heat flux. The limited degree of separation is due to a narrow boiling range of propane and n-butane (41.4 K at atmospheric conditions), in addition to limited heat transfer area. The reflux ratio is plotted for each measurement in Figure 7.2. The reflux ratio increases with heat flux, as more liquid is condensed.

59 60 7 RESULTS

o ------1------1------1------1------1------1______1500 2000 2500 3000 3500 4000 4500 5000

Wall heal flux (W/m2K)

Figure 7.1: Experimental results: Variation of separation (propane) with wall heat flux

0.5

0.45

0.4

0.35

Z 0.3

*3 0.25 ii > 0.2

0.15

0.1

0.05 0 1500 2000 2500 3000 3500 4000 4500 5000

Wall heat flux (W/m2K)

Figure 7.2: Experimental results: Variation of reflux ratio with wall heat flux

Experimental and Theoretical Study of Reflux Condensation 7.1 Experimental results 61

In Figure 7.3, the predicted liquid composition of propane in the reflux stream is plotted against the saturated composition at the measured temperature and pressure. The saturated composition is higher than the predicted value for all the measurements; thus the reflux liquid stream is slightly sub-cooled.

Predicted reflux composition (kmole/kmole)

Figure 7.3: Experimental results: Comparison between predicted and saturated reflux liquid composition (propane)

Remarks about the measurements

The experimental results are compared to the numerical model, and presented in Section 7.2. There are, however, some issues regarding the measurements worth considering. Figures 7.1 and 7.2 show that the measurements have been performed with heat fluxes around 2 and 4 kW/m2. The main focus while operating the rig, was to stabilise the flow measurements. Stable operation limited the variation of wall heat flux. Statistical uncertainty of the measured liquid flow rate is high, as illustrated in Figure 7.4. The figure shows the distribution of the collected data. The flow was checked with ultra-sound measurements, and a fluctuating nature was observed. The unstable

Experimental and Theoretical Study of Reflux Condensation 62 7 RESULTS operation of the flow meters is not caused by the flow meters, but by the process itself. The instabilities are caused by uneven distribution of refrigerant (water) in the condenser and test section. The flow rate of water is kept at a low level to limit heat flux in the test section. Uncertainty increases at decreasing volume flow and is high compared with the un certainty in the measuring unit itself (Table 5.1).

20 1------1------1------1------1------r 1------r Reflux + 18 . ++ Return o

16 I 14 + + 1 12

•a

& 6

4 + 2 + 0 _l______I______I______L. J______L_ 0 5 10 15 20 25 30 35 40 45 50 Flow rate (1/h)

Figure 7.4: Statistical uncertainty of liquid volume flow measurements

The parameter estimation method described in Section 6.4 exploits the uncertainty of the volume flow meters to estimate most probable values. Differential pressure measurements are disregarded due to liquid holdup in the feed lines. An improved rig will include two absolute pressure transmitters, instead of the differential pressure transmitter. The composition measurements undertaken in the gas chromatograph depend strongly on the quality of the samples withdrawn from the test rig. The design of the sample ports was insufficient, and there were difficulties in extraction of test samples. The problem consisted of liquid holdup in the sample tubes and valves, and a significant amount of flushing was necessary to ensure a correct sample. This flushing influences

Experimental and Theoretical Study of Reflux Condensation 7.2 Experimental results compared with numerical calculations 63 the filling of the test rig, and a decision was made to only take a few samples. The composition measurements were used to check the estimated composition from the data analysis program. The experiments which was subject to composition measure ments are denoted as al50797, a050897 and cl20897. Improvements on the experimental rig are suggested in Chapter 9 and Appendix H.

7.2 Experimental results compared with numerical calculations

Each measurement is compared to calculations performed by the numerical model. The measured properties at the top of the unit and the wall heat flux are used as input to the model, which calculates the dephlegmator from top to bottom. The length of the test section (2m) is used as a stop criterion. The model output are properties and flow rates along the length of the dephlegmator channel. A comparison between measured and calculated temperature and flow rate of both feed and reflux product is presented in Figures 7.5, 7.6 and 7.7. The deviation between measured and calculated properties 1, at the bottom of the test section, is used to evaluate the ability of the model to predict the test dephlegmator. Relative deviation between measured and calculated values for each measurement is listed in Table G.4. The model has not been tuned to fit experimental data, and the correlations for heat- and mass transfer coefficients are used as stated in Equations 4.25,4.26 and 4.27.

Temperature

The agreement between measured and calculated temperature is shown in Figure 7.5. Temperature estimates are generally lower than the measured values. The tendency to under predict temperature is larger for the liquid phase than for the vapor phase.

Flow rate

Model predictions on flow rates fits the measured data well, as displayed in Figures 7.6 and 7.7. The calculated flow rates are, in general, slightly above the measured values. Relative deviation between measured and calculated flow rates are higher for the reflux liquid flow, than the feed vapor flow.

'Relative deviation is reported in percent of measured value in °C for temperature, in kmole/s for flow rate and in kmole/kmole for composition

Experimental and Theoretical Study of Reflux Condensation 64 7 RESULTS

65 -""1------1------;------,------Reflux + Feed o 60 - X'Oo u x ++ .X 2 55 I X /#** 50 O + + u OX + 45 -

X______I______40 ______I______t ______l______40 45 50 55 60 65

Measured temperature (C)

Figure 7.5: Comparison between measured and calculated temperature

12 14 16 18

Measured flow rate (le-5 kmol/s)

Figure 7.6: Comparison between measured and calculated feed flow rate

Experimental and Theoretical Study of Reflux Condensation 7.3 Discussion 65

Measured flow rate (le-5 kmol/s)

Figure 7.7: Comparison between measured and calculated reflux flow rate

7.3 Discussion

The numerical model is capable of predicting the measured data with acceptable precision. The deviations are less than 13% of the measured (or predicted) value for all the experiments, of which the discrepancy is highest for reflux liquid phase properties (Table G.4). Comparison between measured and calculated values show that the model under predicts temperature and over predicts flow rate. This means, in terms of dephlegmator length, that the calculated dephlegmator is too short with respect to temperature. With respect to flow rate, the calculated dephlegmator is too long. A number of issues that affect the model predictions are identified and discussed below.

Uncertainty in measurements

Uncertainty in the measurements have been discussed previously in this section, in Chapters 5 and 6, and in Appendix E. Measurement uncertainty may influence the agreement between model and experiments. The low reliability of the flow

Experimental and Theoretical Study of Reflux Condensation 66 7 RESULTS

measurements are not recognized from the comparison in the previous section, as the agreement on flow rate is satisfactory.

Inconsistency in measurements

Measurements of process temperature are done by thermocouples, inserted in capil lary tubes in the test rig. The measurement points are not at the exact entrance- and exit positions of each stream, due to physical constraints in the rig. This leads to inconsistency between the measured- and calculated temperature. Measurement of reflux liquid temperature is done in the outlet of the liquid collec tor, as shown in Figure 7.8. This installation was done to avoid interruption of the liquid film in the test section, and to avoid unwanted influence of vapor phase on the measurements. The position of the calculated liquid temperature is also indicated. Similarly, the actual measurement point for feed vapor temperature deviates from the point calculated by the model.

£ Refrigerant

"Calculated" liquid temperature...... •" "Calculated" vapor Measured liquid temperature temperature......

Liquid- Measured vapor temperature

Reflux liquid Feed vapor

Figure 7.8: Temperature measurement points of vapor inlet and reflux liquid outlet section

Heat transfer from the feed vapor to the reflux liquid, may partially explain the differ ence in measured and calculated temperature. This is supported by observing that the

Experimental and Theoretical Study of Reflux Condensation 7.3 Discussion 67 deviation increases with temperature difference, as shown in Figure 7.9. The linear trendlines are included to highlight the effect of increased temperature difference.

Vapor o

Tv - T1 (measured) (K)

Figure 7.9: Liquid- and vapor temperature deviation as function of TVtmeas — Ti!meas

The process data is exclusive for this particular rig. Uncertainty and inconsistency in the measurements, may lead to erroneous conclusions with respect to the model pre dictions. Verification of the model by comparison with data from similar equipment is desired. Such data is not presently available, with exception of the reported data in Section 4.4. The model estimates on data from Di Cave et al. [21] agrees with the calculations reported in this section for liquid phase composition. The model under predicts the feed composition reported in Reference 21, as opposed to predictions made here. The deviations on feed composition in both data sets are, however, small.

Model basis

An empirical correlation, not based on fundamental physics, is susceptible to errors when applied to different processes than it was originally developed for. This is the case for the heat- and mass transfer correlations used in the model, which may be termed semi-empirical. These correlations were developed empirically for a specific geometry, based on a theoretical understanding and dimension analysis. The vapor

Experimental and Theoretical Study of Reflux Condensation 68 7 RESULTS heat transfer coefficient is calculated from a correlation for single-phase flow in a tube. No correction is made due to the two-phase flow, such as vapor-liquid interface effects and increased relative velocity. Prediction of the mass transfer coefficient is based on analogy to heat transfer. Table 7.2 lists average deviation between measured- and calculated values in percent of the measured values. The heat- and mass transfer coefficients, av and k, have been increased with 40% and 100%, respectively, in the two last columns of the table. The increment of heat- and mass transfer coefficients reduces the relative deviation on liquid temperature and composition in both phases. The effect on vapor temperature and flow rate of liquid and vapor, is a reversing of sign on the deviation. The change of sign on the relative deviations does not occur at the same value of heat- and mass transfer coefficients. Table 7.2 shows that increased heat- and mass transfer coefficients improve the pre dictions from the numerical model. The effect of increased heat- and mass transfer coefficients is not consistent for all variables, and does not alone explain the deviation between measured and calculated values.

Measured Average deviation [%]

value &v,ref * kref 1.4ttV)rey, 1.4A‘ref ^^v,ref 9 X -7.83 -5.32 -3.40 Gi -1.54 0.61 5.41 Ti 3.23 2.09 1.21 y -0.99 -0.70 -0.59 Gv -0.36 -0.09 0.50 Tv 1.12 0.33 -1.50

Table 7.2: Effect of heat- and mass transfer coefficient (Average deviation between measured- and calculated values in percent of measured value)

Constant pressure is assumed in the model. Pressure drop leads to lower dew- and boiling point temperature, about 4 K/bar for an equimolar mixture of propane and n- butane at 10 bar. This effect supports the model tendency to predict lower feed/reflux temperature, as the calculations are initiated at a slightly too high pressure. The actual pressure drop is below 10 mbar, and does not explain the temperature deviations.

Experimental and Theoretical Study of Reflux Condensation 7.3 Discussion 69

The reflux liquid product is assumed to be saturated. Composition of a saturated liquid is, at constant pressure, dependent on temperature, as shown in Figure 7.10. A modest error in temperature has a significant effect on the predicted composition.

-0.02 -

Liquid composition, propane (kmole/kmole)

Figure 7.10: Saturated liquid composition dependency on temperature for propane/n- butane mixtures at 10 bar pressure

Figure 7.3 indicates that the liquid is sub-cooled. This sub-cooling may be estimated, as illustrated in Figure 7.11, using Equation 7.1.

( f)Tsat \ -1 ^ (Z"" - Spred) (7.1)

This deviation is calculated and displayed in table 7.3. The model assumption of satu rated liquid has a limited effect, and does not alone explain the observed discrepancies between measured and predicted reflux liquid temperature.

Experimental and Theoretical Study of Reflux Condensation 70 7 RESULTS

x x

Figure 7.11: Illustration of sub-cooling in a T-x plot at constant pressure

Measurement dTi,sub T;L,meas Til,calc 1100697 0.4683 2.52 al 10697 0.3628 1.97 bl10697 0.3373 2.35 al20697 0.1735 2.64 al30697 0.1734 2.99 b170697 0.3637 2.02 bl80697 0.1730 1.38 al90697 0.0212 1.09 al50797 0.0051 1.76 b010897 0.0450 0.87 b040897 0.0323 1.90 a050897 0.0433 1.47 6050897 0.0075 -0.05 cl20897 0.0081 1.46 al 30897 0.0933 0.94

Table 7.3: Estimated sub-cooling, due to difference in predicted and saturated liquid composition, and difference in measured- and calculated temperature

Experimental and Theoretical Study of Reflux Condensation 7.3 Discussion 71

The interface perimeter, Si, is set equal to the tube perimeter, Stest, in the model. The actual perimeter, and vapor heat transfer area, is smaller due to the liquid film. This effect is small, as illustrated in Figure 7.12, where the reduced relative heat transfer area, Si!Stest, is plotted as a function of void fraction.

Void fraction (-)

Figure 7.12: Reduction of heat transfer area with void fraction in a circular tube

Model input is initial values taken from the measurements. The experimental flow rate of top product is predicted indirectly from measurements of liquid- and bypass flow rates. The sensitivity of model predictions to this parameter is studied here. Table 7.4 indicates that the flow rates are over predicted by the model (averages are 0.4% for vapor and 1.5% for liquid). A 5% reduction of the initial value top product flow rate leads to changes in the predicted properties as listed in the last column of Table 7.4. The predicted feed flow rate is strongly dependent on the initial value of top product. The remaining properties at the bottom of the dephlegmator are reasonably unaffected by a modest reduction in this initial value. Refrigerant is not included in the model, and heat transfer is treated as a predefined heat flux or wall temperature. The heat flux depends on the cold side fluid proper ties, and was modified to vary along the test section. Local temperature difference measurements are not available in the test section. Average differences for each of

Experimental and Theoretical Study of Reflux Condensation 72 7 RESULTS

Measured Average deviation [%] value Gy,top — Kneas &v,top ~ X -7.83 -7.63 Gi -1.54 -1.60 Ti 3.23 3.14 y -0.99 -0.69 Gv -0.36 3.71 Tv 1.12 0.96

Table 7.4: Effect of initial value, vapor flow rate (Average deviation between measured- and calculated values in percent of measured value) the four cooling jacket sections are available, but discrepancy between the assumed linearly varied heat flux and the real heat flux are impractical to establish. Solution method and Taylor expansion of thermodynamic relations may affect the model predictions. This effect is important if the thermodynamic derivatives with respect to temperature and composition are large. An example of this is a mixture of propane and nitrogen (inert gas), with a significant difference in properties of the two compounds. The propane-butane mixtures used in this work have similar properties and the thermodynamic derivatives are small. Droplets were observed through the sight glass above the test section. The entrain ment of droplets increases with vapor velocity up to the flooding point. The detected entrainment, in the operating ranges, is modest, but no visual observation is possible in the test section itself. Entrainment and deposition are not included in the model. Entrainment contributes to thinning of liquid film and increased vapor-liquid interface area.

Summary The deviations between measured- and predicted temperature are caused by a com bination of the topics discussed in this section. Inconsistency in the temperature measurements is the dominant contributor. Prediction of heat- and mass transfer coefficients biases the results to some extent, but does not alone explain the observed discrepancy. The saturated liquid assumption, neglecting pressure drop, interface perimeter deviation, treatment of cold process side and entrainment do not affect the results significantly.

Experimental and Theoretical Study of Reflux Condensation 8 Case studies using the numerical model

Case studies are used to relate theory to industrial processes, using the numerical model described in Chapter 4. This exercise should enhance understanding of the physics involved in reflux condensation. Experimental data from the laboratory, reported in Chapter 7, supports the validity of the model. This chapter describes a number of cases, where dephlegmator technology may be appropriate. Different dephlegmator geometry is chosen for each case. A general description valid for all cases is given in Section 8.1. Each case are treated in Sections 8.2 to 8.4, where case specific data is listed. The first case, a de-methanizer, is thoroughly reported, while the other cases are reported in a briefer form. Improved design, including other fin types, is discussed in Section 8.5.

8.1 General case study description

The chosen geometry is that of a plate-fin heat exchanger. This choice is done to relate the cases to actual process equipment. The PFHE is considered to be the most suitable unit in operation as a dephlegmator. The aim of this study is to design a plate-fin dephlegmator, and to predict the effect on performance by variations in process parameters. High flow rate enhances heat and mass transfer, and the different designs are, therefore, performed with a high flow rate at the inlet of the unit. This is limited by the flooding point. The model calculates plain fins with case dependent fin and plate geometry. The core geometry is restricted by the maximum stacking height, width and length available from manufacturers of aluminium PFHEs. Maximum stacking height and width are commonly about 1.2 m, and maximum length are about 6 m. These restrictions are due to thermal expansion and material strength of heat exchanger cores in the brazing operation. Heat removal is treated, in the model, as a predefined wall temperature or heat flux. The constant heat flux option is used here, as it approximates a situation with constant temperature difference between coolant and condensing fluid. The heat flux depends on the conditions on the cold side, which is not included in the model. In real processes, available cold process streams may be used to supply condensing duty . The nature of heat transfer in these instances depends on the flow rate, composition, pressure and temperature of the cold stream.

73 74 8 CASE STUDIES USING THE NUMERICAL MODEL

Some of the results in this chapter are presented with several digits after the decimal point. This is done to show differences in simulation runs with small overall changes, and does not reflect the accuracy in the reported numbers.

8.2 Demethanizer

The first case to be investigated is separation of methane from heavier hydrocarbons. The process is common in hydrocarbon processing industries, such as natural gas process plants and ethylene plants.

Design of de methanizer

APCI [39] recommends dephlegmator technology for pre-separation in conventional distillation processes. The scenario here is the following: A natural gas flow of 3000 kmole/h is to be refined to export gas. Water, COg and HgS is removed upstream, and the gas is assumed to enter the pre-separation unit at 40 bar. The temperature- composition diagram in Figure 8.1 is included to show the temperature boundary of the two-phase region at varying pressure.

P = lObar — P = 20bar — P = 30bar... P = 40bar —

Composition, methane (kmole/kmole)

Figure 8.1: Methane-ethane T-x diagram

Experimental and Theoretical Study of Reflux Condensation 8.2 De methanizer 75

Assuming a methane content of 70 mole percent in the feed stream, the case is simplified to a binary mixture of methane and ethane. This assumption, with the heavy fraction consisting only of ethane, is a conservative approximation. By choosing a top product composition of 95 mole percent methane, and following the design procedure in Section 4.3, top flow rate, heat flux and core geometry is set. The specifications are listed in Table 8.1.

Parameter Unit Pressure P 40 bar Feed flow rate F 3000 kmole/h Feed composition z/eec2 0.70 kmole/kmole Top product composition Ytop 0.95 kmole/kmole Heat flux 9 500 W/m2 Core height H 1.2 m Core width W 1.2 m Fin height h 5.0 mm Fin spacing P 1.0 mm

Table 8.1: Base case input data for de-methanizer case

The first run gives a flooding factor significantly above the allowed 0.7, even with maximum fin- and core geometry. This indicates the need for a division of the feed stream into more than one unit. By following the design procedure, the solution obtained is displayed in Table 8.2, for a dephlegmator with feed flow rate capacity of one quarter of the initial specifications. A pre-separation plant will, in this case, consist of four heat-exchanger cores with a total cooling duty of 3.66 MW. The composition profile 1 of liquid and vapor phase throughout the length of the dephlegmator unit is indicated in Figure 8.2.

‘The points on each curve in Figures 8.2,8.8 and 8.9, indicate step length as decided by the numerical integration method in the model

Experimental and Theoretical Study of Reflux Condensation 76 8 CASE STUDIES USING THE NUMERICAL MODEL

Parameter Unit Feed flow rate F 759.6 kmole/h Top product flow rate V 442.8 kmole/h Liquid flow rate L 316.8 kmole/h Liquid composition X 0.35 kmole/kmole Core height H 1.20 m Core width W 1.20 m Core length L 5.86 m Fin height h 8.0 mm Fin spacing P 4.0 mm Fin thickness t/in 0.7 mm Plate thickness tV 1.2 mm Hydraulic diameter D/> 4.55 mm Heat removed q 914.3 kW Flooding factor c 0.65 - Temperature difference, bottom dTfcot 6.43 K Temperature difference, top dTt0p 8.58 K

Table 8.2: Design of dephlegmator (De-methanizer case)

Experimental and Theoretical Study of Reflux Condensation 8.2 De methanizer 77

Methane - ethane (q = 500 W/m2, P = 40 bar)

0.9 ,r

0.7 -

0.6 -

0.5 -

0.4 -

Distance from top of unit (m)

Figure 8.2: Methane - ethane composition profile

Sensitivity of de methanizer case

Variation of one parameter in the model affects the remaining parameters. Table 8.3 summarises the effect of these variations in the de-methanizer case. The initial values at the top of the dephlegmator is kept constant, when not subject to variation. The required feed rate and composition is also kept constant. The arrows denote increase (<*), decrease (x) and no significant change (-) of the parameters.

Parameter Flooding Length Duty Xreflux V r kmole-i [-] [m] [W] '■kmole J [-] Pressure s y y y y y Heat flux y - X y y - y top y y y y X y Fin spacing y \ y - y - Fin height y X y - y -

Table 8.3: Effect on design of parameter variation

Experimental and Theoretical Study of Reflux Condensation 78 8 CASE STUDIES USING THE NUMERICAL MODEL

The different process parameters have been varied in the vicinity of the design values to study the effect on heat transfer area and separation. The results from the sensitivity analysis are shown in Tables 8.4, 8.5 and 8.6. In addition, some of the results are highlighted in Figures 8.3, 8.4 and 8.5. Variation of the process pressure is presented in Table 8.4. Refrigeration at low pressure is costly due to low temperature, the reward being increased purification. This is indicated in the pressure variation plot, Figure 8.3. An increase in liquid methane content of 16.7 mole percent is induced by a pressure increase from 20 to 40 bar. The reflux ratio is also increased, and the pressure increment increases the refrigeration duty with 4.6%. The duty is measured as heat transferred from the dephlegmation process, and does not refer to actual refrigeration cost. The refrigeration cost depend on process temperature, which, at the top of the dephlegmator, increases from 178K to 193K as a result of the increased pressure. The flooding factor increases with increasing pressure.

Liquid composition (Cl) —t- Reflux ratio —x- Duty ---■*■

0.6 -

Base case—-

Pressure (bar)

Figure 8.3: Sensitivity of de-methanizer design to process pressure

The total heat transfer area on the condensing side varies with heat flux as displayed in Figure 8.4, where the area is shown as length of heat exchanger. The plot shows that heat flux can be increased, giving a smaller unit, with a penalty in overall duty.

Experimental and Theoretical Study of Reflux Condensation 8.2 Demethanizer 79

p L Xreflux Tfeed Treflux Flooding q V 20 5.06 0.21 230.2 221.1 0.58 874.1 0.50 25 5.23 0.25 233.4 226.4 0.59 879.8 0.55 30 5.46 0.28 238.7 231.3 0.60 895.2 0.59 35 5.63 0.32 242.9 234.8 0.62 900.3 0.62 40 5.86 0.35 244.4 238.0 0.65 914.3 0.70 44 6.03 0.38 246.0 239.8 0.68 922.7 0.75

Table 8.4: Sensitivity of de-methanizer design to process pressure

The effect of variation of wall heat flux is shown in Table 8.5. The liquid methane composition increases slightly with heat flux. Reflux ratio and flooding factor are fairly unaffected by variation in heat flux.

-— Base case

Heat flux (W/mA2)

Figure 8.4: Sensitivity of de-methanizer design to wall heat flux

The effect of altering the top product composition is shown in Table 8.6. Figure 8.5 displays the variations of heat exchanger area and reflux ratio. There is a significant increase in length of the unit with increasing top product purity. Flooding factor and reflux ratio increase with top composition (keeping the feed conditions constant),

Experimental and Theoretical Study of Reflux Condensation 80 8 CASE STUDIES USING THE NUMERICAL MODEL

Qwall L Xrefiux Flooding q V 400 7.18 0.3498 0.65 896.2 0.70 500 5.86 0.3504 0.65 914.3 0.70 600 4.99 0.3515 0.65 934.3 0.69 800 3.83 0.3577 0.65 962.2 0.70 1000 3.13 0.3651 0.65 976.7 0.69

Table 8.5: Sensitivity of de-methanizer design to wall heat flux while the reflux composition is unaltered by the changes in top product composition.

0.75

0.5

0.25

Base case 0 0.9 0.91 0.92 0.93 0.94 0.95 0.96 0.97 0.98 0.99

Top product

UUUUUUU1 1DDDDDDD DDDDDDDDDDDDDDDDDDDDOI Fin type 1 DDDODDDDDOQDDDDDDODQDQODDDODDDDDDD DDDDDDDDDDDDDDOQDQDDD

DDDDDOODDDDDDQD Fin type 2

Fin type 3

Fin type 4

Feed vapor - reflux liquid

Figure 8.10: New design of PFHE dephlegmator internal geometry

Experimental and Theoretical Study of Reflux Condensation 90 8 CASE STUDIES USING THE NUMERICAL MODEL

Experimental and Theoretical Study of Reflux Condensation 9 Recommendations for future work

A research work always identify new questions and issues to study in further depth. Some of these issues are identified at an early stage. Others are discovered during the course of work, due to new understanding of the problem at hand. New findings are addressed, but limited resources (time, financial, personnel) may prevent obtaining a solution to all of them. Identification of new issues and topics to investigate in future work is, more or less, the nature of research, and should be regarded as a part of the results. This work has uncovered a number of topics to pursue in the future work. There are still a number of challenges in this area of technology. Flooding, heat- and mass transfer, distribution of fluid and instability are important phenomena that are difficult to cover in one model or experimental rig. This thesis has focused on the thermodynamic processes for binary mixtures. Extension of this work to model multi-component systems on both process- and refrigerant side is needed. The re ported results in this thesis does not indicate potential problems in expanding the model. An important issue, that should be given priority, is investigation of the fluid dynamic processes in connection with flooding, instability between flow channels and distri bution of fluid. Design and operation of dephlegmators are restricted by these major obstacles. In this context, description of the refrigerant side is important. Future work on dephlegmator should, therefore, focus on real geometries, such as plate-fin heat exchangers. The different forms of instability and flow regimes that occur must be studied, and both theoretical and experimental work is required. Fluid dynamic work enables improved internal design of plate-fin layers to avoid flooding and insufficient distribution of fluid. Focus on local flooding point is impor tant. The different areas of research, to be pursued in future work, should end up in a “unit operation ” model for dephlegmators. The potential for energy savings with dephlegmators depends on process integration. This integration may not be properly evaluated unless a dephlegmator unit operation is available in a process simulation tool. Specific suggestions to future research, regarding the current experimental and theo retical work, are listed in Appendix H.

91 92 9 RECOMMENDATIONS FOR FUTURE WORK

Experimental and Theoretical Study of Reflux Condensation 10 Conclusions

The following conclusions are derived, based on the work described in this thesis: Separation of a binary mixture in a reflux condenser test rig is demonstrated. 15 experiments with separation of propane and n-butane mixtures are reported. Limited degree of separation is obtained in the experiments, due to limited area and narrow boiling point range of the test mixture. The numerical model reproduces the experiments, within reasonable accuracy. Devi ation, between measured and calculated properties, is less than 6% of the measured temperature, and less than 5% of the measured flow rate. The model work is based on mechanistic models of physical processes, and has not been calibrated or tuned to fit the experimental data. Difference between measured and calculated temperature at the bottom of the test section, is mainly due to inconsistency between measured- and calculated points. In addition, heat- and mass transfer coefficients calculated by the model are low due to two-phase flow effects not included in the model. Model assumptions (constant pressure and saturated liquid) do not contribute signifi cantly to discrepancy between measured and calculated properties. The numerical model is applied to a number of processes. These case studies show that the required heat transfer area increases rapidly with increments in top product composition (light component). Flooding limits the amount of reflux liquid. The dephlegmator is, therefore, suitable for separation of feed mixtures that are rich in light components. Gliding temperature in the process enables the use of top product as refrigerant, with subsequent energy savings as a result. Flooding is recognized as a major design constraint in dephlegmators. A new design to overcome this constraint in a plate-fin dephlegmator is proposed.

93 94 10 CONCLUSIONS

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[42] D.I. Limb and B.A. Czamecki. Reflux-exchange process lifts propane recovery at Aussie site. Oil & Gas Journal, pages 35 - 40,1987.

[43] A. Rojey. Optimisation energetique des precedes de separation en raffinage et en traitement de gaz naturel. Revenue de 1‘lnstitut Francois du Petrole, 49(6):627 - 638, Novembre - Decembre 1994.

[44] Industrial heat exchangers. Commercial brochure by IMI Marston ltd., 1991.

[45] Brazed aluminium plate-fin heat exchangers. Commercial brochure by ALTEC International, April 1995.

[46] G. Schultz and U. Werner. Gas Separation Using the Membrane Rectification Technique. Desalination, 51:123- 133, July 1984.

[47] G.F. Hewitt and N.S. Hall-Taylor. Annular Two-Phase Flow. Pergamon Press, 1970.

Experimental and Theoretical Study of Reflux Condensation REFERENCES 99

[48] F.M. White. Fluid Mechanics. McGraw-Hill International Editions, 2nd edition, 1986.

[49] W.H. Press, B.P. Flannery, S.A. Teukolsky, and W.T. Vetterling. Numerical Recipes in C. Cambridge University Press, 1989.

[50] D.Y. Peng and D.B. Robinson. A New Two-Constant Equation of State. Ind. Eng. Chem., Fundam., 15(l):59-64, 1976.

[51] W.M. Kays and M.E. Crawford. Convective Heat and Mass Transfer. McGraw- Hill, Inc., 2nd edition, 1980.

[52] R.L. Webb. Principles of Enhanced Heat Transfer. John Wiley & Sons, Inc., 1994.

[53] H.S. Maehlum. Autocad drawing, 1997. SINTEF Energy.

[54] K.G. Gustavsen. Micrografx designer drawing, 1997. SINTEF Energy.

[55] R.J. MacDonald and C.S. Howat. Data Reconciliation and Parameter Estimation in Plant Performance Analysis. AIChE Journal, 34(1):1 - 8, January 1988.

[56] G. Soave. Equilibrium constants from a modified Redlich-Kwong equation of state. Chemical Engineering Science, 27:1197- 1203,1972.

[57] P. Beranek and I. Wichterle. Vapour-Liquid Equilibria in the Propane-n-Butane System at High Pressures. Fluid Phase Equilibria, 6:279 - 282,1981.

[58] ISO 5168. Measurement of fluid flow - Estimation of uncertainty of a flow-rate measurement, 1978.

[59] R.P. Benedict. Fundamentals of Temperature, Pressure, and Flow Measure ments. John Wiley & Sons, 3rd edition, 1984.

[60] B.N. Taylor and C.E. Kuyatt. Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results. Technical report, NIST technical Note 1297, September 1994. 1994 Edition.

[61] I. Guttman, S.S. Wilks, and J.S. Hunter. Introductory Engineering Statistics. John Wiley & Sons, Inc, 3rd edition, 1971.

Experimental and Theoretical Study of Reflux Condensation 100 REFERENCES

Experimental and Theoretical Study of Reflux Condensation APPENDICES

101 102 Appendix

Experimental and Theoretical Study of Reflux Condensation A Patents using dephlegmator technology

This appendix lists patents found in literature search on dephlegmators [2,3]. Author Country Year Process Aleksev, V.P. et al. RUS 1996 Fractionated alcohol prodn. on single shift operation

APCI USA 1997 Moderate purity oxygen production process used in cryogenic distillation of air

APCI USA 1994 Precooling for ethylene recovery in dual demethanizer fractionation systems

APCI USA 1994 Recovering ethylene from mixture with hydrogen and 1-3C hydrocarbon(s)

APCI USA 1991 Dephlegmator process for the recovery of helium

APCI USA 1988 Dephlegmator process for carbon dioxide-hydrocarbon distillation

APCI USA 1988 Dephlegmator process for nitrogen rejection from natural gas

APCI USA 1988 Process for the recovery of hydrogen/heavy hydrocarbons from hydrogen-lean feed gases

APCI USA 1987 Process for recovery and purification of C3+/C4+ hydrocarbons using segregated phase separation and dephlegmation

103 104 Appendix A

APCI USA 1986 Process for recovery and purification of C3-C4+ hydrocarbons using segregated phase separation and dephlegmation

APCI USA 1986 Staged multicomponent refrigerant cycle for a process for recovery of C3+ hydrocarbons

APCI USA 1985 Dual dephlegmator process to separate and purify syngas mixtures

APCI USA 1984 Recovering C4+ hydrocarbons using a dephlegmator

APCI USA 1983 Process for recovering C44. hydrocarbons using a dephlegmator

APCI USA 1979 Separation of hydrogen containing gas mixtures

Carter, R. USA 1930 Art of recovering blended fuels

Comb.Petro. "Borzesti" ROM 1982 Dephlegmation-concentration of the product from the top of fractionation-distillation towers

Chem.-Tech. Inst. USSR 1976 Automatic control of the working conditions of a dephlegmator during distillation

Daido Hoxan Inc. JAP 1996 High purity N2 gas production method

Experimental and Theoretical Study of Reflux Condensation Appendix A 105

Dainippon IC JAP 1995 Preparation of 2-hydroxycarboxylic acid oligomers in high yields

Demoulins, H.D. et al. UK 1923 Purifying hydrocarbons

FA Holstein NET 1991 Distn. of fruit brandy to reduce cyanide content

Gaz de France FRA 1989 Fluid heating installation having an associated absorption heat pump cycle

Gaz de France FRA 1983 Improvements to a fluid heating equipment with a thermal cycle associated to an absorption heat pump

Heyl, G.E. UK 1926 Cracking hydrocarbons

Huers AG GER 1996 Cleaving tert. butyl alcohol in distillation column

Kothe U. 1987 GER Fine distilling appts

Kuraksiin, V.M. et al. RUS 1996 Rectification column for fermented solns. with reduced size

Matsushita et al. JAP 1997 Water distiller for absorption type heat pump used at home

Morrell, J.C. UK 1975 Treatment of oil shales

Morrell, J.C. AUS 1979 Distillate fuels from oil shales

Nosek, F. CZR 1938 Furnace retort for cracking

Experimental and Theoretical Study of Reflux Condensation 106 Appendix A

Overton, P.C. AUS 1937 Coal distillation plant

Schmitt, K. GER 1982 Device for thawing an evaporator of an absorption system with hot gas

Schultz, E. et al. AUS 1927 Recovery of light oil from organic materials

Smirnov, V.I. RUS 1996 Rectification plant for sepn. of liq. according to boiling point

Stone and Webster USA 1990 Cryogenic separation of gaseous mixtures

Trumble, M.J. UK 1926 Distilling coal shale, etc.

Trumble, M.J. USA 1924 Process of producing gasoline from solid material extraction and cracking of shale oil

VEB Waermeanlag. GER 1983 Process for raising the heat output of absorption heat pump

Wallace, G.W. USA 1924 Cracking and hydrogenating hydrocarbons

Experimental and Theoretical Study of Reflux Condensation B Matrix elements in model solution procedure

This appendix lists the non-zero elements of the coefficient matrix, A, the variable vector, x, and the residual vector, R in Equation 4.23 in Chapter 4. The symbolic manipulation was performed with MAPLE V. The thermodynamic (Taylor expanded) functions, the heat- and mass transfer corre lations and the composition sums have been substituted into this set of equations.

Ai,i = Si Ai,2 = Al,4 - A2,i = dx A2,3 = &r P,Ni

A2,6 =

A3,i = As,2 = A4,i = A4)3 = A5,1 - Si( hVta,refy CPv,a,yTv 4" CPv,ayTv^ref CPv,bTv 4" CPv,bTv,ref ~hVyb,ref 4" yCpv,bTv ycPv,bTv,ref 4" y^v,b,rej')ly dh v f dh v As,2 = ^•u,re/ 4“ CpyPy CpvTVtTef 4" y- yref p,t,n2 P,T,N2 ( dhv \ / dhv\ \dN2J P,T,Nj y V dN2 ) p,T,Ni

( dhv \ _ / dhv\ As,4 = \dNi) Pj^-2 \dN2) pit,n1_

As,5 = Gvcpv A6,1 = Si{ .a.rcf y CPv,a.y'%'v 4" CPv.ayTv.rcf CPv,bT?; -(- Cpv>bTv>rej ~hv,b,ref 4" yCPv,bTv — ycPv,bTV,rej 4" Z/^u,6,re/)/ 2/

107 108 Appendix B

dz X / dhi X Ae,3 hi,ref 4" CpiTl Cp\T[,ref 4" 9T ) p,Ni \ dNi) p,t,n2

Experimental and Theoretical Study of Reflux Condensation Appendix B 109

K-y,'! - (§)pjV| Ti + (S)P,„, T,'’t +y)Sl/y R3 =

T, + (f^)pM rW + »)*/» R4 =

Rs = otvyTi H“ kyrcjcpvfiTv kyrejcpv^TVirej -j- kyrejhv^^rej 1 T/cp^r^e/

%,6,r«y - A T,,r,/cp^

~^~k p pj' '^'lirefc'Pvib'Fv,ref ~ k p ^iref^v^ref — kycpvfiTv

+kycpVibT Vjref &£/^u,6,re/)/V Re = Si[oLvyTv otvyTi + kyTefCpv^Tv kyTejcpv^Tv^rGj 4- kyrefhv^jrej +*

~^k Tltrefcpv,bTVtref — k TiirefhVib,ref ~ kycpVtbTv

+kycpVtbTv>ref kyhVjbjTej cxiyTi -4- &iyTw^ / y

Experimental and Theoretical Study of Reflux Condensation 110 Appendix B

Experimental and Theoretical Study of Reflux Condensation C Gas chromatograph measurements

This appendix describes the composition measurements on the test rig, described in Section 5.2. A gas chromatograph (GC), Hewlett-Packard - HP 5890A, determines the composition of the different streams in the test facility. The GC consists of 3 columns and a thermal conductivity detector. In addition, the GC system contains an integrator, HP 3392A, and an event control unit, HP 19405A, for valve operation. The vapor and liquid sample ports are displayed in Figure 5.1. The liquid sample is evaporated in a boiler before sampling. Details of the GC configuration are listed in Table C.l. Samples are extracted from the test rig when stable operation is established.

Unit Description Column 1 5 ft 1/8 inch, 30% DC 200 Silicon oil on 60/80 mesh Cromosorb P-AW Column 2 6 ft 1/8 inch, Porapak Q, 80/100 mesh Column 3 10 ft 1/8 inch, Molecular sieve 13X, 45/60 mesh Injection loop 100 /i 1 Injektor temperature 70°C Detector temperature 250°C Column temperature 70°C Valve temperature 70°C Carrier gas rate 25 ml/min, Helium Reference gas rate 45 ml/min, Helium

Table C.l: Gas chromatograph configuration

The composition of the test gas is determined through response factors, R;, for each component, i. The composition is calculated with Equation C.l, where R, is the response factor determined by the calibration gas, and A; is the measured area under each peak of the chromatograph print. For a binary mixture, Equation C.l reduces to Equation C.2. To calibrate the GC, a calibration gas with known composition is used. The gas was weighted to a known vapor composition, and the ratio of the response factors is determined, on the basis of this known calibration gas composition, by Equation C.3. This ratio is used to calculate the composition of the different test samples extracted from the test rig. An example of a gas chromatograph print is

111 112 Appendix C displayed in Figure C.l.

RiAi Z; — (C.l)

For a binary mixture:

Zl (C.2) H'Ai + A2 Ri z\A% (C.3) R2 A\ — z\A\ dz\ = (S+ w,dM+§^dAl

Ai (a2<^) - jg2dAj - j£dA2) (C.4) (Ai^ + A2)

Ri AiA2dzi zj2A2dAi d + R2 (ziAi — A;+)2 (z\A\ — A;)2 z\ dA 2 (C.5) z\A\ — Ai

VJ i S 5

KS8:£$£fe5:$ £

5SS

TrrrT -H-r Uf fl»wei»tVPS.—

Figure C.l: Sample of gas chromatograph printout

Experimental and Theoretical Study of Reflux Condensation Appendix C 113

A total of 9 calibration runs were performed with a binary mixture of propane and normal-butane to determine the ratio of the response factors, and the variation of the variables in Equation C.2. Accuracy of the composition measurements is determined on the basis of Equation C.4. Equations C.4 and C.5 are standard partial derivative functions to estimate propagation of uncertainty. The standard deviation is used as an estimate for the uncertainty in the areas (Ai,A2). The uncertainty in the composition of the calibration gas is estimated to be 1 mole percent based on the uncertainty analysis in Appendix D. A summary of the calculated uncertainty is given in Table C.2.

Unit Equation Value Number of calibration runs - 9 Molar composition propane PR 0.49 ft C.3 1.416 Ai - 1238533 JnEAlziEA^2 d(Ai) y n(n-l) 4267.6 a2 - 1826922 JnEAlz(LArf d(A2) V n(n-l) 9466.1 <%ft) C.5 0.069

Table C.2: Calibration data for GC measurements on C3A1-C4

The problems of obtaining correct samples are described in Section 7.1. A decision was made to only perform control of the calculated composition on a few measure ments. These experiments are denoted as al50797, a050897 and cl20897 and listed in Appendix G. The measured liquid composition is lower than calculated, but the extraction of liquid samples poses a rather large uncertainty in the chromatograph measurements. This uncertainty is difficult to quantify, but the reported results are within 8% of the calculated value, even for the liquid composition. It is, therefore, fair to say that the agreement between measured and calculated composition is acceptable.

Experimental and Theoretical Study of Reflux Condensation 114 Appendix C

Experimental and Theoretical Study of Reflux Condensation D Accuracy in Peng-Robinson and Soave-Redlich-Kwong cubic equations of state for propane-n-butane mixtures

The thermodynamic calculations in this thesis are based on the Peng-Robinson [50] cubic equation of state, Equation D.l. In this appendix, the equation is compared to the Soave-Redlich-Kwong [56] equation of state, Equation D.2, and experimental VLE-data [57] for the propane/n-butane binary system at different pressures. For mixtures, the mixing rules are given in Equations D.3 - D.5. The pure component attraction parameter and covolume are found from Equations D.l and D.2 at the critical point (Equations D.6 - D.10).

Peng-Robinson EOS [50]

Soave-Redlich-Kwong EOS [56] RT | a(T) (D.2) v — b v(v + b)

a = (D.3) i j b = 53 X*bi (D.4) i (D.5)

a,i(T) = ai(TCli)a(Tr,aj) (D.6) %(T) = %(%,;) (D.7) (D.8)

kpr = 0.3746 + 1.5423V,- - 0.2699w? (D.9)

ksrk = 0.480 + 1.574v,-— 0.176v^ (D.10)

115 116 Appendix D

Beranek and Wichterle [57] claim the following accuracy in their experimental work:

• Temperature = 0.01 K (absolute)

• Pressure = 0.001 MPa (absolute)

• Concentration =1.5% (relative)

Pressure and vapor composition were calculated from the experimental values of temperature and liquid composition, using both the SRK and the PR equation. The root mean square deviation between experimental and calculated P and y were calculated with different values of the interaction coefficient, f>i3. The plots in Figure D. 1 and D.2 show distinct minima with respect to the uncertainty in pressure and vapor composition. The vapor composition is chosen as the guiding parameter. The minimum for ^-uncertainty in the PR-plot is a RMS value of 0.14% for 6ij = -0.0086. The corresponding minimum for the SRK equation is 0.20% for &ij = -0.148. Beranek and Wichterle [57] found Sij = -0.146. for the SRK equation. The lower RMS value for the Peng-Robinson equation of state supports the choice of this correlation. The Ax and Ay in Table D.l suggest an uncertainty on composition predictions of ± 1 mole percent. The experimental- and calculated composition values are plotted in Figure D.3.

Experimental and Theoretical Study of Reflux Condensation Experimental Appendix and

Theoretical RMS RMS 0.002 Figure 0.004 0.002 0.004 0.008 0.01 Figure 0.01

Study -0.03 -0.03

ir - - - - - of D.2:

-0.025 Reflux -0.025 D.l:

Condensation

Tuning

Tuning -0.02 -0.02

-0.015 -0.015

Soave-Redlich-Kwong of

SRK Interaction Interaction

Peng-Robinson -0.01 PR -0.01

interaction

interaction -0.005 -0.005

parameter parameter

EOS 0 0

EOS coefficient, 0.005 0.005 coefficient,

0.01 0.01

0.015 0.015

Sij

0.02 0.02 117 118 Appendix D

0.9 - Liquid composition Vapor composition 0.8 -

0.7 -

0.6 -

0.5 -

0.4 -

Experimental propane composition

Figure D.3: Experimental and calculated values using Peng-Robinson EOS with tuned interaction coefficient, 8{j = -0.0086

Experimental and Theoretical Study of Reflux Condensation Appendix D 119

P [bar] T [K] xCs ,ex p y Ci,exp xc3,pr yc3,pr Ax Ay 3.540 303.14 0.096 0.261 0.1019 0.2570 0.0059 -0.0040 4.005 303.14 0.164 0.388 0.1700 0.3847 0.0060 -0.0033 4.681 303.14 0.257 0.530 0.2658 0.5253 0.0088 -0.0047 5.910 303.14 0.437 0.707 0.4307 0.6987 -0.0063 -0.0083 9.474 303.14 0.867 0.942 0.8571 0.9485 -0.0099 0.0065 9.935 303.14 0.910 0.958 0.9077 0.9679 -0.0023 0.0099 5.669 323.10 0.066 0.155 0.0685 0.1631 0.0025 0.0081 7.279 323.10 0.225 0.411 0.2255 0.4343 0.0005 0.0233 9.304 323.10 0.399 0.635 0.4084 0.6437 0.0094 0.0087 10.884 323.10 0.541 0.742 0.5412 0.7539 0.0002 0.0119 12.912 323.10 0.700 0.853 0.7007 0.8572 0.0007 0.0042 14.930 323.10 0.857 0.931 0.8481 0.9338 -0.0089 0.0028 15.687 323.10 0.905 0.954 0.9008 0.9579 -0.0042 0.0039 9.063 343.17 0.065 0.144 0.0648 0.1380 -0.0002 -0.0060 10.035 343.17 0.133 0.267 0.1331 0.2609 0.0001 -0.0061 11.275 343.17 0.216 0.400 0.2172 0.3877 0.0012 -0.0123 14.131 343.17 0.411 0.601 0.3985 0.5972 -0.0125 -0.0038 16.388 343.17 0.535 0.710 0.5308 0.7130 -0.0042 0.0030 19.389 343.17 0.691 0.833 0.6930 0.8280 0.0020 -0.0050 22.361 343.17 0.854 0.918 0.8393 0.9148 -0.0147 -0.0032 23.573 343.17 0.903 0.944 0.8949 0.9450 -0.0081 0.0010 13.812 363.38 0.063 0.122 0.0609 0.1155 -0.0021 -0.0065 15.090 363.38 0.128 0.232 0.1274 0.2254 -0.0006 -0.0066 16.735 363.38 0.207 0.351 0.2097 0.3430 0.0027 -0.0080 20.577 363.38 0.399 0.559 0.3891 0.5476 -0.0099 -0.0114 23.683 363.38 0.527 0.669 0.5219 0.6673 -0.0051 -0.0017 28.005 363.38 0.691 0.797 0.6898 0.7940 -0.0012 -0.0030 32.184 363.38 0.847 0.891 0.8338 0.8898 -0.0132 -0.0012 34.136 363.38 0.900 0.933 0.8947 0.9290 -0.0053 -0.0040

Table D.l: Comparison of thermodynamic data from experiments [57] and Peng- Robinson EOS

Experimental and Theoretical Study of Reflux Condensation 120 Appendix D

P [bar] T [K] xCs,exp y C3,exp *c3,srk y Cs,SRK Ax Ay 3.540 303.14 0.096 0.261 0.1036 0.2557 0.0076 -0.0053 4.005 303.14 0.164 0.388 0.1734 0.3856 0.0094 -0.0024 4.681 303.14 0.257 0.530 0.2702 0.5280 0.0132 -0.0020 5.910 303.14 0.437 0.707 0.4343 0.7021 -0.0027 -0.0049 9.474 303.14 0.867 0.942 0.8489 0.9472 -0.0181 0.0052 9.935 303.14 0.910 0.958 0.8979 0.9657 -0.0121 0.0077 5.669 323.10 0.066 0.155 0.0660 0.1541 -0.0000 -0.0009 7.279 323.10 0.225 0.411 0.2266 0.4320 0.0016 0.0210 9.304 323.10 0.399 0.635 0.4097 0.6444 0.0107 0.0094 10.884 323.10 0.541 0.742 0.5408 0.7549 -0.0002 0.0129 12.912 323.10 0.700 0.853 0.6967 0.8572 -0.0033 0.0042 14.930 323.10 0.857 0.931 0.8402 0.9319 -0.0168 0.0009 15.687 323.10 0.905 0.954 0.8914 0.9551 -0.0136 0.0011 9.063 343.17 0.065 0.144 0.0598 0.1254 -0.0052 -0.0186 10.035 343.17 0.133 0.267 0.1303 0.2524 -0.0027 -0.0146 11.275 343.17 0.216 0.400 0.2162 0.3828 0.0002 -0.0172 14.131 343.17 0.411 0.601 0.3989 0.5966 -0.0121 -0.0044 16.388 343.17 0.535 0.710 0.5305 0.7135 -0.0045 0.0035 19.389 343.17 0.691 0.833 0.6905 0.8282 -0.0005 -0.0048 22.361 343.17 0.854 0.918 0.8341 0.9134 -0.0199 -0.0046 23.573 343.17 0.903 0.944 0.8886 0.9429 -0.0144 -0.0011 13.812 363.38 0.063 0.122 0.0547 0.1024 -0.0083 -0.0196 15.090 363.38 0.128 0.232 0.1235 0.2164 -0.0045 -0.0156 16.735 363.38 0.207 0.351 0.2082 0.3379 0.0012 -0.0131 20.577 363.38 0.399 0.559 0.3903 0.5476 -0.0087 -0.0114 23.683 363.38 0.527 0.669 0.5235 0.6691 -0.0035 0.0001 28.005 363.38 0.691 0.797 0.6906 0.7962 -0.0004 -0.0008 32.184 363.38 0.847 0.891 0.8334 0.8910 -0.0136 -0.0000 34.136 363.38 0.900 0.933 0.8937 0.9293 -0.0063 -0.0037

Table D.2: Comparison of thermodynamic data from experiments [57] and Soave- Redlich-Kwong EOS

Experimental and Theoretical Study of Reflux Condensation E Estimation and treatment of uncertainty in measure ments

A result of a given measurement is, usually, only an estimate of the specific value of the quantity subject to the measurement. The result is, therefore, only complete when supplemented with a quantitative announcement of its uncertainty. The errors are commonly [58-61] divided into four groups:

• Spurious errors

• Random errors

• Constant systematic errors

• Variable systematic errors

The following describes the different groups of errors accompanied by a statement of propagation of such uncertainties related to the current study.

Spurious errors Spurious errors are those related to malfunction of instruments or human errors. These errors are usually difficult to detect and are not incorporated into the statistical uncer tainty analysis. A thorough analysis of the measurement chain, from measurement point to conversion of data, and documented measurement routines minimise the risk of having spurious errors.

Random errors

A series of measurements of any kind produces a scatter of individual values around the mean value. The magnitude of the deviations from the mean value is quantified as a statistical uncertainty. In large populations, the data points are assumed to vary, by chance, in a manner approaching a normal distribution. The statistical uncertainty is derived by statistical analysis of repeated measurements [59]. The mean value of a population of repeated measurements is derived from Equation E.2. This is the best estimate for the true value of the measured parameter. The Central Limit Theorem states that the distribution of the sum of values, having iden tical distribution, approaches the normal distribution [61]. In a small population of measurements, the standard deviation is not obtainable, and the student-t probability

121 122 Appendix E distribution is often used as a correction to the normal distribution. The student-t parameter, tu, in Equation E.3 inflates the precision index, S, and reduces the effect of underestimating the standard deviation [59]. The student-t parameter for the given probability and degrees of freedom is reproduced in Table E.2. The measured value with specified uncertainty is given by Equation E.l.

X{ XiX ± Me, (E.l) 1 n Xi ; z (E.2) n k= 1 e; Si (E.3) 1 1 2 Si N—1) £(l"‘"5r‘)2 (E.4)

Constant systematic errors

Systematic uncertainty is fixed and gives a constant output being either too high or too low compared to the true value. The uncertainties in question may be known, and can be corrected for by calibration, or they may be of unknown magnitude and sign. The value of a systematic uncertainty may be evaluated by an approximation to a standard deviation. This value is determined by experience, knowledge and/or pure judgment of the uncertainty involved. A basis for this evaluation may include:

• Specifications from the manufacturer of equipment

• Calibration to known values

• Experience from previous measurements

• General knowledge or experience with equipment

• Other means

Variable systematic errors Variable systematic errors are identified when the output of an instrument vary in the operating range of the instrument. Flow measurements are typical, where the error increases as the flow rate decreases towards the lower limit of the measurement range. An example of this type of error is displayed in Table 5.1.

Experimental and Theoretical Study of Reflux Condensation Appendix E 123

Propagation of errors It is recommended in Reference 58 to disregard error contributions which are signifi cantly smaller than the largest component. If the smaller error is less than one fifth of the larger error, it is, as a general rule, permissible to disregard this source of error. When the measurement result has a functional dependence on several variables, Equa tion E.5, random errors may be combined using Equation E.6 for standard deviation. The covariance term, reproduced in Equation E.7, is used whenever there is an inter dependency between variables.

y y(*^l?*^2)****? ^n) (E.5)

(E.6) i=1 .7=2+1 1 ” _ _ S Xj) 53 — **] ~ xi\ (E.7) n

The combined estimate of uncertainty in the measurements, is obtained using the root- sum-square method, although the separate components are also listed in Table E.l. This is done because there is no consensus on how to properly present the combined uncertainty [58]. The statistical uncertainty is represented with a typical value, as it differs between measurements. This value is printed for every measurement in Appendix G.

Experimental and Theoretical Study of Reflux Condensation 124 Appendix E

Uncertainty (in % of measured value) Measurement Random Calibration Precision Sum Bypass vapor flow 1.64 4 0.007 4.32 Reflux liquid flow 8.03 2 0.003 8.28 Return liquid flow 2.52 1.5 0.003 2.93 Thermocouple type T 0.01 0.04 0.06 0.07 Thermocouple type E 0.01 0.1 0.04 0.29 Pressure 0.09 0.1 0.006 0.13 Differential pressure 0.001 5 0.003 5.00 Condenser liquid flow 3.50 2 - 4.03 Test section liquid flow 0.11 2 0.003 2.00 Heater duty 0.69 1.2 0.005 1.38

Table E.l: Uncertainty in measurements (within a 95% confidence level for random errors)

V *90% *95% *98% V *90% *95% *98% 1 6.314 12.706 31.821 18 1.734 2.101 2.552 2 2.920 4.303 6.965 19 1.729 2.093 2.539 3 2.353 3.182 4.541 20 1.725 2.086 2.528 4 2.132 2.776 3.747 21 1.721 2.080 2.518 5 2.105 2.571 3.365 22 1.717 2.074 2.508 6 1.943 2.447 3.143 23 1.714 2.069 2.500 7 1.895 2.365 2.998 24 1.711 2.064 2.492 8 1.860 2.306 2.896 25 1.708 2.060 2.485 9 1.833 2.262 2.821 26 1.706 2.056 2.479 10 1.812 2.228 2.764 27 1.703 2.052 2.473 11 1.796 2.201 2.718 28 1.701 2.048 2.467 12 1.782 2.179 2.681 29 1.699 2.045 2.462 13 1.771 2.160 2.650 30 1.697 2.042 2.457 14 1.761 2.145 2.624 40 1.684 2.021 2.423 15 1.753 2.131 2.602 60 1.671 2.000 2.390 16 1.746 2.120 2.583 120 1.658 1.980 2.358 17 1.740 2.110 2.567 oo 1.645 1.960 2.326

Table E.2: Probability factors of the T distribution with v degrees of freedom [59]

Experimental and Theoretical Study of Reflux Condensation F Data analysis of measurements

Data collected from the test rig is used as input to the data analysis program. The different measurements are listed in Table F.2. Data files from the data logger, in volts, is converted to measurement data by calibra tion information for each measurement point. The conversion routine also calculate the statistical distribution of each measurement point. The measurements from the test rig are temperature, pressure, volume flow rates and heater duty. For a complete analysis of each measurement, some properties must be converted indirectly from the measured data. These properties are composition, enthalpy, molar flow rate, heat flux and cooling duty.

Qcond r- V- Top condenser

Qtest

Figure F.l: Conceptual sketch of test rig

Enthalpy, composition and flow rate (in terms of kmole/s) is calculated from the mea surements, by using conservation equations on the test rig. There are 7 independent

125 126 Appendix F conservation equations (Equations El - E7) for mass, composition and energy for the three main parts of the test rig, shown in Figure F.l. In addition, there are 4 ther modynamic relations connecting enthalpy, composition, pressure and temperature, Equations F.8 - F. 11.

Boiler: L + R-(F + B) =■ 0 (F.l)

Lx + R xr — (F + B)z = 0 (F.2)

Lhp + RhR — (jF + B)hp + qboil = 0 (F.3)

Test section: F-V-L = 0 (F.4) Fz — V y — Lx = 0 (F.5) Fhp — V hy — Lhp — qtest = 0 (F.6)

Total rig:

qboil Qtest — Qcond Qloss 0 (F.7)

Enthalpy: hp (F.8) hy (F.9) h-L (F.10) hp f(TR,P,xR) (F.ll)

In order to solve the properties of the five streams, a set of equations and measurements must be solved. Originally, composition measurements were included, but problems with the fluid sample ports (Appendix C) prevents the use of these measurements. This gives a number of 11 measurements applicable for solving the stream properties, Table F.l.

Experimental and Theoretical Study of Reflux Condensation Appendix F 127

Variables # Measurements and equations # FVLRB kmole/s 5 LRB 1/h 3 zy xx# - 4

hy h# hr J/kmole s 4 ({boil q cond q test q/oss W 4 Qboil Qcondi QtesZ W 3 T# Ty TL Tr °C 4 T# Ty TL T# °C 4 p Pa 1 P Pa 1 Conservation, mass kmole/s 2 Conservation, comp. kmole/s 2 Conservation, energy W 3 Enthalpy J/kmole 4 Sum 22 Sum 22

Table F.l: Summary of variables, measurements and equations in data analysis

No Name Symbol Unit Manual/on 1 Boiler, liquid °C O 2 Boiler, vapor '^boil,v °C O 3 Reflux flow (liquid) T L °c O 4 Top product, liquid TR °c O 5 Top product, vapor Ty °c O 6 Partial condenser, in Ttest,in °c O 7 Partial condenser, 3/4 Ttesi,3/4 °c O 8 Partial condenser, 1/2 T test,1/2 °c O 9 Partial condenser, 1/4 Tfest,l/4 °c O 10 Partial condenser, out T test,out °c O 11 Condenser, in Tcond,in °c O 12 Condenser, out Tcond, out °c 0 13 Test section, 01 Toi °c o 14 Test section, 02 Tq2 °c o 15 Test section, 03 Tos °c 0 16 Test section, 04 Tq4 °c o 17 Test section, 05 Tqs °c 0 18 Test section, 06 Toe °c o 19 Test section, 07 Tot °c 0

Experimental and Theoretical Study of Reflux Condensation 128 Appendix F

No Name Symbol Unit Manual/on 20 Test section, 08 Tos °c O 21 Test section, 09 Tog °c O 22 Test section, 10 Tio °c O 23 T Surroundings T$ur °c O

24 Bypass volume flow bypass m3/h O 25 Cooling water, test section Vtesi 1/h O 26 Reflux volume flow ^reflux 1/h o 27 Top product volume flow 1/h o 28 System pressure P Pa o 29 Differential pressure dP Pa o 30 Boiler heat duty kW o 31 Inlet composition z kmole/kmole M 32 Top product composition y kmole/kmole M 33 Reflux composition X kmole/kmole M 34 Cooling water, condenser ^cond 1/s M

Table F.2: Measurement points on test rig

Experimental and Theoretical Study of Reflux Condensation G Summary of measurements

Tables G.l - G.3 contain a summary of the measurements in this study. Each mea surement is listed individually, with the mean value of each data point and statistical distribution. The first table of each reported measurement contains raw data con verted from volt signals to measurement values by calibration data. The next table presents the maximum likelihood values, and finally characteristic data for heat flux and flloding are presented. Some of the results in this appendix are presented with several digits after the decimal point. This is done to show differences in experiments with small overall changes in composition and flow rate, and does not reflect the accuracy in the reported numbers.

The average deviation in Table G.4 is calculated by Equations G. 1 and G.2.

— 1 A = -5>i (G.l)

__ 1 n Aabs = - 53 I A, | (G.2) II Measurement Heat flux < ytop Zfeed <|r 1100697 4782.2 0.078 0.356 al10697 4340.5 0.071 0.324 6110697 4182.6 0.070 0.319 al20697 3815.7 0.067 0.289 al30697 3924.8 0.072 0.334 6170697 4362.2 0.071 0.319 6180697 1843.2 0.029 0.119 al90697 1684.6 0.025 0.107 a!50797 3781.6 0.058 0.269 6010897 2208.6 0.032 0.279 3050897 4349.8 0.057 0.276 6050897 2134.9 0.027 0.126 C120897 1682.7 0.017 0.078 3130897 1698.6 0.021 0.101

Table G.l: Summary of measurements (1)

129 130 Appendix G

P Heat flux Oboii attest Qcond qio SS bar W/m2 w w w % 1100697 10.87 4782.2 2599.9 643.0 1870.1 3.3 al 10697 10.28 4340.5 2545.1 583.6 1705.0 10.1 bl10697 11.06 4182.6 2501.7 562.4 1861.2 3.1 al20697 9.03 3815.7 2501.6 513.1 1918.6 2.8 al30697 10.44 3924.8 2289.0 527.7 1706.9 2.4 b170697 9.49 4362.2 2289.5 586.5 1440.1 11.5 b180697 10.16 1843.2 2180.8 247.8 1862.7 3.2 al90697 10.27 1684.6 2180.9 226.5 1880.1 3.4 al50797 10.58 3781.6 2288.0 508.5 1798.5 -0.8 bO10897 10.11 2208.6 2228.2 297.0 1800.1 5.9 b040897 11.58 4511.0 2650.7 606.6 1838.6 7.8 a050897 11.48 4349.8 2592.7 584.9 1823.9 7.1 b050897 9.66 2134.9 2472.7 287.1 2096.0 3.6 cl20897 12.17 1682.7 2838.6 226.3 2542.2 2.5 al30897 11.82 1698.6 2290.2 228.4 1984.7 3.4

Table G.2: Summary of measurements (2)

Inlet Top product Reflux liquid T z F T y V T X R 1100697 328.0 0.680 1.37e-4 322.8 0.758 1.01e-4 326.7 0.462 3.61e-5 al 10697 325.4 0.684 1.32e-4 320.6 0.755 9.99e-5 324.1 0.465 3.24e-5 bl10697 328.7 0.682 1.32e-4 324.3 0.752 9.98e-5 327.6 0.462 3.18e-5 a120697 319.4 0.702 1.25e-4 315.6 0.770 9.71e-5 318.4 0.469 2.81e-5 al30697 326.0 0.687 1.18e-4 321.3 0.759 8.84e-5 324.7 0.470 2.95e-5 6170697 323.1 0.664 1.32e-4 318.4 0.735 1.00e-4 321.8 0.443 3.19e-5 b180697 326.2 0.674 1.28e-4 324.3 0.702 1.14e-4 325.6 0.431 1.36e-5 al90697 325.3 0.690 1.28e-4 323.5 0.715 1.16e-4 324.7 0.459 1.24e-5 a150797 327.7 0.659 1.35e-4 324.2 0.717 1.07e-4 326.9 0.444 2.86e-5 bO10897 325.6 0.666 1.30e-4 323.4 0.698 1.14e-4 324.9 0.442 1.64e-5 6040897 333.4 0.628 1.58e-4 329.5 0.687 1,24e-4 332.6 0.416 3.45e-5 a050897 332.9 0.624 1.55e-4 329.4 0.681 1.21e-4 332.1 0.417 3.35e-5 6050897 323.7 0.649 1.43e-4 322.3 0.675 1.27e-4 323.2 0.437 1.61e-5 cl20897 327.8 0.774 1.79e-4 326.3 0.791 1.66e-4 327.2 0.559 1.30e-5 al30897 330.0 0.756 1.42e-4 325.1 0.777 1.29e-4 326.3 0.550 1.30e-5

Table G.3: Summary of measurements (3)

Experimental and Theoretical Study of Reflux Condensation Appendix G 131

Run Deviation [%] number X L T, y F Tv t100697 -12.92 -3.88 4.71 -2.00 -0.87 3.12 al10697 -9.91 -4.01 3.87 -1.39 -0.98 2.91 bl10697 -11.68 -2.52 4.32 -1.75 -0.53 1.85 al20697 -11.76 2.49 5.83 -1.89 0.56 -1.69 al30697 -12.35 -2.03 5.80 -1.98 -0.42 2.22 M70697 -10.14 -3.13 4.15 -1.42 -0.68 2.32 bl80697 -7.51 3.68 2.63 -0.62 0.55 -1.13 al90697 -5.03 -3.23 2.11 -0.23 -0.23 0.96 al50797 -7.80 -2.80 3.27 -0.97 -0.96 1.96 bO10897 -3.64 -2.44 1.68 -0.23 -0.38 0.76 b040897 -8.77 -4.06 3.20 -1.02 -0.95 2.22 a050897 -6.84 -2.39 2.49 -0.82 -0.45 1.10 b050897 0.23 -1.86 -0.10 0.09 0.00 0.46 cl20897 -5.83 7.69 2.70 -0.45 0.45 -1.59 al30897 -3.44 -4.62 1.77 -0.12 -0.42 1.30

A -7.83 -1.54 3.23 -0.99 -0.36 1.12 ^abs 7.86 3.39 3.24 1.00 0.56 1.71

Table G.4: Relative deviation between measured values and model calculations (in percent of measured value)

Experimental and Theoretical Study of Reflux Condensation 132 Appendix G

File ’tl00697.tex ’ processed at Sun Nov 2 11:12:551997

Data (75 data points) from files ,tl00697.raw ’ and ’tl00697.inn\

Measurement Unit Mean value a95% Relative value Tboil,l °C 51.07 5.62e-02 1.10e-03 Tboil,v °C 54.86 4.85e-02 8.85e-04 T L °C 53.54 4.82e-02 9.00e-04 T R °C 40.09 4.47e-02 l.lle-03 Tv °C 49.66 4.65e-02 9.37e-04 Tfestyin °C 35.39 1.51e-02 4.27e-04 Ttest,3/4 °c 37.60 2.32e-02 6.18e-04 Ttest, 1/2 °c 39.91 2.61e-02 6.54e-04 Ttest,l/4 °c 42.25 3.02e-02 7.14e-04 T test,out °c 44.93 3.78e-02 8.40e-04 Tcond,in °c 18.98 3.40e-02 1.79e-03 T condjOut °c 28.19 4.79e-02 1.70e-03 Toi °c 48.08 8.15e-02 1.69e-03 Tq2 °c 50.06 4.79e-02 9.56e-04 Tq3 °c 49.49 4.12e-02 8.33e-04 Tq4 °c 50.31 4.07e-02 8.09e-04 To5 °c 46.94 4.56e-02 9.70e-04 Toe °c 49.02 4.07e-02 8.30e-04 Tqt °c 44.98 4.34e-02 9.64e-04 Tos °c 46.22 3.51e-02 7.59e-04 Tog °c 42.34 2.76e-02 6.52e-04 Tio °c 47.19 3.60e-02 7.64e-04 T$Ur °c 25.87 6.18e-02 2.39e-03 VB 1/h 156.74 2.47e+00 1.57e-02 Viest 1/h 58.10 4.02e-02 6.92e-04 Vr lAi 12.40 1.97e-01 1.59e-02 Vy 1/h 39.52 6.00e-01 1.52e-02 P kPa 1086.59 9.76e-01 8.98e-04 96oz'Z W' 2600.02 8.03e-01 3.09e-04

Experimental and Theoretical Study of Reflux Condensation Appendix G 133

Maximum-likelihood values: New value Old value Difference a F kmole/s 1.37e-04 1.30e-04 7.12e-06 3.52e-06 V kmole/s 1.01e-04 9.67e-05 4.51e-06 2.12e-06 L kmole/s 3.61 e-05 3.35e-05 2.61e-06 5.33e-07 R kmole/s 1.19e-04 1.14e-04 4.61e-06 1.73e-06 B kmole/s 1.75e-05 1.73e-05 1.03e-07 2.73e-07

T F K 3.28e+02 3.28e+02 1.97e-02 4.85e-02 Tv K 3.23e+02 3.23e+02 -8.95e-03 4.65e-02 TL K 3.27e+02 3.27e+02 -7.59e-03 4.82e-02 T R K 3.13e+02 3.13e+02 -5.62e-03 4.47e-02 z kmole/kmole 6.80e-01 6.87e-01 -6.49e-03 1.00e-02 y kmole/kmole 7.58e-01 7.61e-01 -3.44e-03 1.00e-02 X kmole/kmole 4.62e-01 4.71e-01 -8.81e-03 1.00e-02

Xfl kmole/kmole 7.46e-01 7.50e-01 -3.51e-03 1.00e-02 W 2.60e+03 2.60e+03 -1.10e-01 8.03e-01 Qcond W 1.87e+03 1.87e+03 -2.46e-02 6.55e+01 fltest w 6.43e+02 6.43e+02 -8.50e-02 4.45e-01 flioss w 8.68e+01 8.68e+01 -5.47e-05 3.04e+00 P Pa 1.09e+06 1.09e+06 -6.45e+01 9.76e+02 Condenser water flow rate 174.45 1/h Cooling duty on test section part 1 148.54 W Cooling duty on test section part 2 155.78 W Cooling duty on test section part 3 157.54 W Cooling duty on test section part 4 181.25 W Average heat flux 4782.22 W/m2 Number of theoretical stages 1.36 Wallis flooding factor 0.77 Heat loss on total rig (energy) 86.78 W ( 3.34 %) Stream X-calc Xpred Flow rate (kmole/s) Reflux liquid 0.4619 3.6074e-05 Return liquid 0.7464 1.1871e-04 Feed vapor 0.6801 1.3733e-04 Bypass vapor 0.6801 1.7452e-05 Top product vapor 0.7578 1.0126e-04

Experimental and Theoretical Study of Reflux Condensation 134 Appendix G

File ’all0697.tex ’ processed at Sun Nov 2 11:13:001997

Data (70 data points) from files ’al 10697.raw ’ and ’al 10697.inn\

Measurement Unit Mean value a95% Relative value TboiU °C 48.50 3.63e-02 7.49e-04 Tboil,v °C 52.22 2.71e-02 5.19e-04 TL °c 50.96 2.79e-02 5.47e-04 T R °c 37.89 2.48e-02 6.56e-04 TV °c 47.45 2.47e-02 5.22e-04 Ttest,in °c 33.89 2.27e-02 6.71e-04 Ttest, 3/4 °c 35.95 2.43e-02 6.76e-04 T(esi, 1/2 °c 38.05 2.46e-02 6.46e-04 Ttest, 1/4 °c 40.31 2.78e-02 6.88e-04 Ttesi.oui °c 42.88 2.55e-02 5.96e-04 Tconrf,m °c 15.15 3.56e-02 2.35e-03 Tcond,ouf °c 24.98 3.36e-02 1.34e-03 Toi °c 45.75 7.59e-02 1.66e-03 Tq2 °c 47.66 3.80e-02 7.96e-04 Tq3 °c 47.23 2.53e-02 5.36e-04 Tq4 °c 47.94 2.57e-02 5.37e-04 Tos °c 44.69 3.74e-02 8.38e-04 Tq6 °c 46.50 3.02e-02 6.50e-04 Tq7 °c 42.96 3.97e-02 9.25e-04 Tos °c 44.66 2.14e-02 4.80e-04 Too °c 41.34 2.00e-02 4.84e-04 Tio °c 45.64 2.30e-02 5.03e-04 T sur °c 23.04 9.93e-02 4.316-03 VB 1/h 167.09 2.84e+00 1.70e-02 1/h 55.96 6.54e-02 1.17e-03 Vfi 1/h 10.80 2.21e-01 2.04e-02 Vy 1/h 39.26 5.78e-01 1.47e-02 P kPa 1028.19 5.71e-01 5.55e-04 C[boiZ W 2863.62 6.90e+01 2.41e-02

Experimental and Theoretical Study of Reflux Condensation Appendix G 135

Maximum-likelihood values: New value Old value Difference a F kmole/s 1.32e-04 1.26e-04 6.44e-06 3.82e-06 V kmole/s 9.99e-05 9.64e-05 3.43e-06 2.17e-06 L kmole/s 3.24e-05 2.94e-05 3.01e-06 6.01e-07 R kmole/s 1.18e-04 1.14e-04 3.52e-06 1.68e-06 B kmole/s 1.77e-05 1.76e-05 8.94e-08 3.00e-07 TF K 3.25e+02 3.25e+02 5.21e-03 2.71e-02 Tv K 3.21e+02 3.21e+02 -2.33e-03 2.47e-02 TL K 3.24e+02 3.24e+02 -2.01e-03 2.79e-02 TR K 3.11e+02 3.11e+02 -1.30e-03 2.48e-02 z kmole/kmole 6.84e-01 6.90e-01 -6.32e-03 1.00e-02 y kmole/kmole 7.55e-01 7.56e-01 -1.85e-03 1.00e-02 X kmole/kmole 4.65e-01 4.72e-01 -6.89e-03 1.00e-02 XR kmole/kmole 7.44e-01 7.46e-01 -2.26e-03 1.00e-02 Qboil W 2.55e+03 2.86e+03 -3.19e+02 6.90e+01 flcond W 1.70e+03 2.02e+03 -3.10e+02 7.05e+01 fltest w 5.84e+02 5.84e+02 -2.18e-01 6.83e-01 flZoss w 2.56e+02 2.64e+02 -7.876+00 1.12e+01 P Pa 1.03e+06 1.03e+06 -1.71e+01 5.71e+02 Condenser water flow rate 176.111/h Cooling duty on test section part 1 133.89 W Cooling duty on test section part 2 136.37 W Cooling duty on test section part 3 146.72 W Cooling duty on test section part 4 166.87 W Average heat flux 4340.54 W/m2 Number of theoretical stages 1.32 Wallis flooding factor 0.76 Heat loss on total rig (energy) 256.45 W (10.08 %)

Stream X-calc Xpred Flow rate (kmole/s) Reflux liquid 0.4654 3.2393e-05 Return liquid 0.7439 1.1759e-04 Feed vapor 0.6837 1.3225e-04 Bypass vapor 0.6837 1.7732e-05 Top product vapor 0.7546 9.9860e-05

Experimental and Theoretical Study of Reflux Condensation 136 Appendix G

File ’bll0697.tex ’ processed at Sun Nov 2 11:13:121997

Data (83 data points) from files ’bl 10697.raw ’ and ’bl 10697.inn ’.

Measurement Unit Mean value <795% Relative value T boil,! °C 51.94 3.38e-02 6.51e-04 ^boil, v °C 55.59 2.80e-02 5.04e-04 TL °c 54.45 2.28e-02 4.19e-04 T R °c 41.52 2.36e-02 5.69e-04 Ty °c 51.15 4.07e-02 7.96e-04 T{est,in °c 39.54 9.95e-02 2.52e-03 Tfest, 3/4 °c 41.25 9.42e-02 2.28e-03 Ttesi,1/2 °c 42.95 9.10e-02 2.12e-03 Ttest, 1/4 °c 44.87 8.24e-02 1.84e-03 '^■test,out °c 46.93 7.64e-02 1.63e-03 Tcond,in °c 19.15 3.84e-02 2.00e-03 T condjOut °c 29.14 3.95e-02 1.35e-03 Toi °c 50.13 1.39e-01 2.78e-03 T02 °c 51.47 5.51e-02 1.07e-03 Tq3 °c 51.39 7.73e-02 1.50e-03 Tq4 °c 52.03 5.74e-02 1.10e-03 To5 °c 48.72 7.15e-02 1.47e-03 Toe °c 50.74 7.80e-02 1.54e-03 To? °c 48.50 6.13e-02 1.266-03 Tos °c 49.19 7.27e-02 1.48e-03 Too °c 46.35 1.09e-01 2.34e-03 Tio °c 49.73 1.30e-01 2.61 e-03 TSUr °c 27.70 3.20e-02 1.15e-03 VB 1/h 163.38 2.23e+00 1.37e-02 Vtest 1/h 66.31 3.43e-01 5.17e-03 VB 1/h 10.62 2.40e-01 2.26e-02 Vy 1/h 42.28 4.37e-01 1.03e-02 P kPa 1106.10 5.83e-01 5.27e-04 Qboil W 2501.68 1.46e-02 5.84e-06

Experimental and Theoretical Study of Reflux Condensation Appendix G 137

Maximum-likelihood values: New value Old value Difference a F kmole/s 1.32e-04 1.32e-04 8.65e-08 3.73e-06 V kmole/s 9.98e-05 1.03e-04 -3.16e-06 1.76e-06 L kmole/s 3.18e-05 2.86e-05 3.24e-06 6.45e-07 R kmole/s 1.18e-04 1.21e-04 -3.24e-06 1.25e-06 B kmole/s 1.83e-05 1.84e-05 -8.59e-08 2.51e-07 Tf K 3.29e+02 3.29e+02 4.63e-03 2.806-02 Ty K 3.24e+02 3.24e+02 -1.08e-02 4.07e-02 TL K 3.28e+02 3.28e+02 -1.21e-03 2.28e-02 TR K 3.15e+02 3.15e+02 1.87e-03 2.36e-02 z kmole/kmole 6.82e-01 6.84e-01 -2.33e-03 1.00e-02 y kmole/kmole 7.52e-01 7.44e-01 7.86e-03 1.00e-02 X kmole/kmole 4.62e-01 4.69e-01 -6.40e-03 1.00e-02 XR kmole/kmole 7.41e-01 7.35e-01 6.07e-03 1.00e-02 Qboil W 2.50e+03 2.50e+03 4.28e-05 1.46e-02

Qcond W 1.86e+03 1.86e+03 5.89e+00 6.49e+01 diest w 5.62e+02 5.68e+02 -5.90e+00 2.94e+00 dZoss w 7.81e+01 7.80e+01 1.07e-02 2.76e+00 P Pa l.lle+06 l.lle+06 4.04e+00 5.83e+02 Condenser water flow rate 159.64 Vh Cooling duty on test section part 1 131.27 W Cooling duty on test section part 2 131.01 W Cooling duty on test section part 3 147.27 W Cooling duty on test section part 4 158.75 W Average heat flux 4182.58 W/m2 Number of theoretical stages 1.32 Wallis flooding factor 0.75 Heat loss on total rig (energy) 78.06 W( 3.12%)

Stream Xcalc ^pred Flow rate (kmole/s) Reflux liquid 0.4624 3.1838e-05 Return liquid 0.7409 1.1812e-04 Feed vapor 0.6818 1.3168e-04 Bypass vapor 0.6818 1.8281e-05 Top product vapor 0.7517 9.9842e-05

Experimental and Theoretical Study of Reflux Condensation 138 Appendix G

File ’al20697.tex ’ processed at Sun Nov 2 11:13:19 1997

Data (40 data points) from files ’al20697.raw ’ and ’al20697.inn ’.

Measurement Unit Mean value a95% Relative value TboilJ °C 43.19 6.35e-02 1.47e-03 Tboil,v °c 46.27 4.59e-02 9.92e-04 T L °c 45.26 5.24e-02 1.16e-03 T R °c 32.54 4.48e-02 1.38e-03 TV °c 42.45 3.43e-02 8.09e-04 T test,in °c 32.60 1.28e-02 3.94e-04 Tfest, 3/4 °c 34.22 1.89e-02 5.52e-04 Ttest,l/2 °c 35.91 1.76e-02 4.90e-04 T test,1/4 °c 37.33 2.39e-02 6.42e-04 Ttest,out °c 38.98 2.06e-02 5.28e-04 T cond^in °c 13.38 4.87e-02 3.64e-03 Tcond,out °c 20.66 5.29e-02 2.56e-03 Toi °c 41.18 1.68e-01 4.08e-03 T02 °c 42.41 6.65e-02 1.57e-03 To3 °c 42.07 3.58e-02 8.51e-04 Tq4 °c 42.66 3.74e-02 8.77e-04 Tos °c 40.21 3.39e-02 8.42e-04 Toe °c 41.53 2.33e-02 5.61e-04 Tq7 °c 39.48 2.62e-02 6.64e-04 Tos °c 39.26 2.72e-02 6.926-04 Tog °c 36.88 2.09e-02 5.67e-04 Tic °c 39.99 2.32e-02 5.80e-04 Tsut °c 28.55 2.79e-02 9.76e-04 v B 1/h 210.13 2.98e+00 1.42e-02 Viesi 1/h 69.38 9.16e-02 1.32e-03 VB 1/h 7.93 3.60e-01 4.54e-02 Vy 1/h 45.90 7.08e-01 1.54e-02 P kPa 902.93 8.34e-01 9.24e-04 S boil W 2501.63 2.41e-02 9.65e-06

Experimental and Theoretical Study of Reflux Condensation Appendix G 139

Maximum-likelihood values: New value Old value Difference a F kmole/s 1.25e-04 1.38e-04 -1.23e05 6.88e-06 V kmole/s 9.71e-05 1.16e-04 -1.85eOS 2.42e-06 L kmole/s 2.81e-05 2.19e-05 6.14e-06 9.96e-07 R kmole/s 1.17e-04 1.35e-04 -1.88e-05 2.09e-06 B kmole/s 1.956-05 1.98e-05 -3.03e-07 2.81e-07 TF K 3.19e+02 3.19e+02 6.99e-03 4.59e-02 Tv K 3.16e+02 3.16e+02 -8.56e-03 3.43e-02 T L K 3.18e+02 3.18e+02 -3.99e03 5.24e-02 TR K 3.06e+02 3.06e4O2 1.46e-02 4.48e-02 z kmole/kmole 7.02e-01 7.076-01 -4.31e-03 1.00e-02 y kmole/kmole 7.70e-01 7.51e-01 1.87e-02 1.00e-02 X kmole/kmole 4.69e-01 4.72e-01 -3.16e-03 1.00e-02 XR kmole/kmole 7.58e-01 7.45e-01 1.39e-02 l.OOe-02 ([boil W 2.50e+03 2.5064-03 2.71e-04 2.41e-02 (\cond W 1.92e+03 1.9264-03 3.76e-01 6.71e4-01

Ttest W 5.13e+02 5.13e4-02 -3.77eO! 6.78e-01 ([loss w 7.00e401 7.006401 5.02e-04 2.45e-iOO P Pa 9.03e+05 9.0364-05 4.66ef01 8.3464-02 Condenser water flow rate 226.55 1/h Cooling duty on test section part 1 130.60 W Cooling duty on test section part 2 135.58 W Cooling duty on test section part 3 114.44 W Cooling duty on test section part 4 132.81 W Average heat flux 3815.66 W/m2 Number of theoretical stages 1.29 Wallis flooding factor 0.74 Heat loss on total rig (energy) 69.97 W ( 2.80 %)

Stream X-calc X-pred Flow rate (kmole/s) Reflux liquid 0.4687 2.8055e-05 Return liquid 0.7585 1.1665e-04 Feed vapor 0.7023 1.2516e-04 Bypass vapor 0.7023 1.9544e-05 Top product vapor 0.7698 9.7106e-05

Experimental and Theoretical Study of Reflux Condensation 140 Appendix G

File ’al30697.tex ’ processed at Sun Nov 211:13:231997

Data (40 data points) from files ’al 30697 .raw’ and ’al30697.inn\

Measurement Unit Mean value <795% Relative value Tboil,l °C 49.32 4.53e-02 9.18e-04 Tboil,v °C 52.79 3.60e-02 6.83e-04 TL °c 51.58 3.50e-02 6.79e-04 TR °c 38.53 2.79e-02 7.25e-04 Tv °c 48.12 2.90e-02 6.03e-04 Ttest,in °c 35.82 1.02e-02 2.85e-04 Ttest,3/4 °c 38.24 3.24e-02 8.47e-04 Ttest, 1/2 °c 40.20 1.93e-02 4.79e-04 Ttest ,1/4 °c 42.26 2.38e-02 5.64e-04 Ttest,out °c 44.64 2.21e-02 4.95e-04 Tcond,in °c 19.94 1.49e-02 7.49e-04 T condyout °c 27.81 4.09e-02 1.47e-03 Toi °c 47.67 1.00e-01 2.10e-03 Tq2 °c 49.23 4.01e-02 8.15e-04 To3 °c 48.68 2.69e-02 5.52e-04 Tq4 °c 49.15 2.73e-02 5.56e-04 Tq5 °c 46.35 5.04e-02 1.09e-03 Toe °c 47.83 2.98e-02 6.22e-04 Tor °c 44.51 3.95e-02 8.87e-04 Tqs °c 45.28 2.15e-02 4.74e-04 Tq9 °c 41.41 5.01e-02 1.21e-03 Tio °c 42.36 6.13e-02 1.45e-03 T$ur °c 27.33 7.06e-02 2.58e-03 VS 1/h 163.91 3.57e+00 2.18e-02 Vtest Vh 51.60 3.23e-02 6.25e-04 Vfi 1/h 9.11 3.44e-01 3.78e-02 Vy lAi 35.78 1.29e+00 3.61e-02 P kPa 1043.62 6.78e-01 6.50e-04 W 2289.05 2.29e+00 9.99e-04

Experimental and Theoretical Study of Reflux Condensation Appendix G 141

Maximum-likelihood values: New value Old value Difference a F kmole/s 1.18e-04 l.lle-04 7.01e-06 6.28e-06 V kmole/s 8.84e-05 8.62e-05 2.20e-06 3.63e-06 L kmole/s 2.95e-05 2.47e-05 4.81e-06 9.36e-07 R kmole/s 1.06e-04 1.04e-04 2.23e-06 3.74e-06 B kmole/s 1.76e-05 1.75e-05 2.54e-08 3.82e-07 TF K 3.26e+02 3.26e+02 5.26e-03 3.60e-02 Tv K 3.21e+02 3.21e+02 -2.32e-03 2.90e-02 TL K 3.25e+02 3.25e+02 -1.90e-03 3.50e-02 TR K 3.12e+02 3.12e+02 -2.16e-04 2.79e-02 z kmole/kmole 6.87e-01 6.94e-01 -6.77e-03 1.00e-02 y kmole/kmole 7.59e-01 7.57e-01 2.48e-03 1.00e-02 X kmole/kmole 4.70e-01 4.73e-01 -3.31e-03 1.00e-02 Xfi kmole/kmole 7.47e-01 7.46e-01 1.16e-03 1.00e-02 QbotZ W 2.29e+03 2.29e+03 -9.87e-02 2.29e+00 Qcond W 1.71e+03 1.71e+03 -6.26e-02 5.97e+01 Qtest w 5.28e+02 5.28e+02 -3.60e-02 3.30e-01 Q/oss w 5.43e+01 5.43e+01 -6.34e-05 1.90e+00 P Pa 1.04e+06 1.04e+06 -9.34e+00 6.78e+02 Condenser water flow rate 186.67 1/h Cooling duty on test section part 1 144.41 W Cooling duty on test section part 2 117.32 W Cooling duty on test section part 3 123.52 W Cooling duty on test section part 4 142.51 W Average heat flux 3924.82 W/m2 Number of theoretical stages 1.33 Wallis flooding factor 0.71 Heat loss on total rig (energy) 54.29 W ( 2.37 %) Stream XcaZc X-pred Flow rate (kmole/s) Reflux liquid 0.4698 2.9537e-05 Return liquid 0.7472 1.0598e-04 Feed vapor 0.6868 1.1796e-04 Bypass vapor 0.6868 1.7561e-05 Top product vapor 0.7592 8.8423e-05

Experimental and Theoretical Study of Reflux Condensation 142 Appendix G

File ’bl70697.tex ’ processed at Sun Nov 2 11:13:30 1997

Data (98 data points) from files ’bl70697.raw ’ and ’bl70697.inn\ In addition 2 serie(s) ignored due to inconsistency in data.

Measurement Unit Mean value ^95% Relative value T boil,l °C 45.98 1.24e-01 2.69e-03 Tboil,v °C 49.91 1.22e-01 2.44e-03 TL °c 48.65 1.20e-01 2.46e-03 TR °c 34.74 1.13e-01 3.26e-03 Tv °c 45.26 1.24e-01 2.73e-03 Ttest,in °c 33.79 1.63e-01 4.83e-03 Ttesi, 3/4 °c 35.71 1.12e-01 3.14e-03 Xiest, 1/2 °c 37.34 1.20e-01 3.22e-03 Ttest, 1/4 °c 39.24 1.17e-01 2.98e-03 T test, out °c 41.29 1.09e-01 2.64e-03 TCond,in °c 17.99 1.44e-01 8.01e-03 Tcond,out °c 24.67 1.34e-01 5.45e-03 Toi °c 43.75 1.29e-01 2.95e-03 Tq2 °c 45.19 1.14e-01 2.53e-03 Tq3 °c 44.87 1.21e-01 2.70e-03 Tq4 °c 45.64 1.24e-01 2.72e-03 Tq5 °c 42.71 1.21e-01 2.84e-03 Toe °c 43.74 1.15e-01 2.63e-03 Tot °c 41.49 1.21e-01 2.92e-03 Tqs °c 41.41 1.16e-01 2.80e-03 Toe °c 39.32 4.00e-01 1.02e-02 Tio °c 40.61 3.67e-01 9.03e-03 Tsur °c 22.26 6.35e-02 2.85e-03 VB Mi 0.46 7.89e-04 1.70e-03 ~Vtest Mi 67.35 5.33e-02 7.91e-04 V r Mi 10.41 3.00e-01 2.89e-02 Vy Mi 24.02 1.80e+00 7.49e-02 P kPa 949.51 2.13e+00 2.25e-03 *iboil W 2565.53 6.06e+01 2.36e-02

Experimental and Theoretical Study of Reflux Condensation Appendix G 143

Maximum-likelihood values: New value Old value Difference a F kmole/s 1.32e-04 9.88e-05 3.32e-05 7.94e-06 V kmole/s 1.00e-04 7.04e-05 2.97e-05 5.27e-06 L kmole/s 3.19e-05 2.84e-05 3.47e-06 8.21e-07 R kmole/s 1.00e-04 7.04e-05 2.97e-05 5.28e-06 B kmole/s 4.56e-08 4.56e-08 9.38e-15 7.75e-ll Tf K 3.23e+02 3.23e+02 6.17e-02 1.22e-01 Tv K 3.18e+02 3.18e4-02 -2.53e-02 1.24e-01 TL K 3.22e+02 3.22e4-02 -2.216-02 1.20e-01 TR K 3.08e+02 3.08e4-02 -2.62e-02 1.13e-01 z kmole/kmole 6.64e-01 6.58e-01 6.65e-03 1.00e-02 y kmole/kmole 7.35e-01 7.42e-01 -6.88e-03 1.00e-02 X kmole/kmole 4.43e-01 4.49e-01 -6.56e-03 1.00e-02 XR kmole/kmole 7.35e-01 7.42e-01 -6.86e-03 1.00e-02 q bon W 2.2964-03 2.5764-03 -2.76e4-02 6.06e4-01 Qcond W 1.4464-03 1.7164-03 -2.66e4-02 5.9764-01 A test W 5.8764-02 5.87e+02 -5.44e-02 4.64e-01 q loss w 2.63e4-02 2.73e4-02 -9.90e4-00 1.1564-01 p Pa 9.4964-05 9.50e4-05 -1.87e4-02 2.1364-03 Condenser water flow rate 219.82 1/h Cooling duty on test section part 1 149.71 W Cooling duty on test section part 2 127.78 W Cooling duty on test section part 3 148.21 W Cooling duty on test section part 4 160.90 W Average heat flux 4362.20 W/m2 Number of theoretical stages 1.32 Wallis flooding factor 0.77 Heat loss on total rig (energy) 262.81 W( 11.48%) Stream Xcalc Xpred Flow rate (kmole/s) Reflux liquid 0.4426 3.1903e-05 Return liquid 0.7349 1.0010e-04 Feed vapor 0.6642 1.3196e-04 Bypass vapor 0.6642 4.5644e-08 Top product vapor 0.7349 1.0005e-04

Experimental and Theoretical Study of Reflux Condensation 144 Appendix G

File ’M80697.tex ’ processed at Sun Nov 2 11:13:361997

Data (100 data points) from files ’bl 80697 .raw’ and ’bl80697.inn\

Measurement Unit Mean value a95% Relative value TioiZJ °C 49.75 2.52e-02 5.07e-04 Tboil,v °C 53.06 8.33e-03 1.57e-04 TL °c 52.44 1.10e-02 2.11e-04 T R °c 39.96 7.88e-03 1.97e-04 Ty °c 51.12 7.73e-03 1.51e-04 Ttesi.in °c 43.99 1.18e-02 2.69e-04 Tfest, 3/4 °c 45.08 1.04e-02 2.31e-04 f'test,l/2 °c 45.90 7.76e-03 1.69e-04 f

Experimental and Theoretical Study of Reflux Condensation Appendix G 145

Maximum-likelihood values: New value Old value Difference a F kmole/s 1.28e-04 1.31e-04 -3.48e-06 1.18e-05 V kmole/s 1.14e-04 1.22e-04 -8.20e-06 1.35e-06 L kmole/s 1.36e-05 8.86e-06 4.72e-06 7.89e-07 R kmole/s 1.14e-04 1.22e-04 -8.20e-06 1.34e-06 B kmole/s 4.79e-08 4.79e-08 -1.97e-14 6.44e-ll T F K 3.26e+02 3.26e+02 3.87e-04 8.33e-03 Ty K 3.24e+02 3.24e+02 -6.51e-04 7.73e-03 TL K 3.26e+02 3.26e+02 -1.12e-04 1.10e-02 TR K 3.13e+02 3.13e+02 5.39e-04 7.88e-03 z kmole/kmole 6.74e-01 6.70e-01 3.47e-03 1.00e-02 y kmole/kmole 7.02e-01 6.87e-01 1.52e-02 1.00e-02 X kmole/kmole 4.31e-01 4.34e-01 -3.23e-03 1.00e-02 XB kmole/kmole 7.02e-01 6.87e-01 1.52e-02 1.00e-02 Qboil W 2.18e+03 2.18e+03 2.19e-05 6.35e-03

Qcond w 1.86e+03 1.86e+03 1.01e-01 6.52e401 fliesi w 2.48e+02 2.48e+02 -1.01e-01 3.20e-01 fl/oss w 7.03e+01 7.03e+01 1.45e-04 2.46e400 P Pa 1.02e+06 1.02e4G6 3.61e400 2.03e402 Condenser water flow rate 202.73 1/h Cooling duty on test section part 1 60.15 W Cooling duty on test section part 2 45.78 W Cooling duty on test section part 3 74.06 W Cooling duty on test section part 4 67.94 W Average heat flux 1843.15 W/m2 Number of theoretical stages 1.12 Wallis flooding factor 0.70 Heat loss on total rig (energy) 70.34 W( 3.23%)

Stream XcaZc Upred Flow rate (kmole/s) Reflux liquid 0.4312 1.3584e-05 Return liquid 0.7024 1.1425e-04 Feed vapor 0.6735 1.2779e-04 Bypass vapor 0.6735 4.7907e-08 Top product vapor 0.7024 1.1420e-04

Experimental and Theoretical Study of Reflux Condensation 146 Appendix G

File ’al90697.tex ’ processed at Sun Nov 2 11:13:43 1997

Data (30 data points) from files ’al90697.raw ’ and ’al90697.inn’ . In addition 20 serie(s) ignored due to inconsistency in data.

Measurement Unit Mean value <7 95% Relative value Tfcoz'z.z °C 48.91 5.66e-02 1.16e-03 T boil,v °C 52.18 1.48e-02 2.83e-04 T L °c 51.59 1.52e-02 2.94e-04 T R °c 39.35 1.32e-02 3.37e-04 Tv °c 50.30 1.26e-02 2.51e-04 Ttest, in °c 44.17 9.98e-03 2.26e-04 Ttest ,3/4 °c 45.36 1.31e-02 2,90e-04 Ttest, 1/2 °c 46.25 1.47e-02 3.19e-04 Ttest, 1/4 °c 47.31 1.41e-02 2.98e-04 Ttest, out °c 48.27 1.08e-02 2.23e-04 Tcond,in °c 20.16 1.53e-02 7.58e-04 T cond,out °c 27.90 1.53e-02 5.47e-04 Toi °c 51.81 6.90e-02 1.336-03 T02 °c 51.77 2.07e-02 4.00e-04 T03 °c 51.83 1.45e-02 2.80e-04 Tq4 °c 52.15 1.28e-02 2.466-04 Tqs °c 50.99 2.32e-02 4.556-04 Tq6 °c 51.73 1.31e-02 2.52e-04 To? °c 50.11 2.26e-02 4.52e-04 Tqs °c 50.77 1.09e-02 2.16e-04 Tq9 °c 48.33 1.59e-02 3.296-04 Tio °c 50.60 2.23e-02 4.426-04 Tsur °c 24.52 6.30e-02 2.57e-03 VS 1/h 0.45 1.03e-03 2.29e-03 Vtest 1/h 47.72 3.69e-02 7.72e-04 Vs 1/h 3.33 4.83e-01 1.45e-01 Vy mi 41.39 9.16e-01 2.21e-02 P kPa 1027.30 3.06e-01 2.986-04 Qboil W 2180.93 1.16e-02 5.326-06

Experimental and Theoretical Study of Reflux Condensation Appendix G 147

Maximum-likelihood values: New value Old value Difference a F kmole/s 1.28e-04 1.28e-04 1.21e-07 1.88e-05 V kmole/s 1.16e-04 1.19e-04 -3.27e-06 2.65e-06 L kmole/s 1.24e-05 9.03e-06 3.39e-06 1.31e-06 R kmole/s 1.16e-04 1.19e-04 -3.27e-06 2.64e-06 B kmole/s 4.75e-08 4.75e-08 -5.94e-15 1.09e-10

TF K 3.25e+02 3.25e+02 3.34e-04 1.48e-02 Tv K 3.23e+02 3.23e+02 -3.20e-04 1.26e-02 TL K 3.25e+02 3.25e+02 -5.28e-05 1.52e-02 TR K 3.13e+02 3.13e+02 1.62e-04 1.32e-02 z kmole/kmole 6.90e-01 6.94e-01 -3.60e-03 1.00e-02 y kmole/kmole 7.15e-01 7.12e-01 3.39e-03 1.00e-02 X kmole/kmole 4.59e-01 4.60e-01 -3.75e-04 1.00e-02 Xj? kmole/kmole 7.15e-01 7.12e-01 3.39e-03 1.00e-02 QboiZ W 2.18e+03 2.18e+03 7.69e-06 1.16e-02 Qcond W 1.88e+03 1.88e+03 5.51e-03 6.58e+01 Qiesi W 2.27e+02 2.27e+02 -5.51e-03 1.75e-01 Qioss W 7.44e+01 7.44e+01 8.64e-06 2.60e+00 P Pa 1.03e+06 1.03e+06 7.46e-01 3.06e+02 Condenser water flow rate 208.84 1/h Cooling duty on test section part 1 65.71 W Cooling duty on test section part 2 49.27 W Cooling duty on test section part 3 58.55 W Cooling duty on test section part 4 53.00 W Average heat flux 1684.62 W/m2 Number of theoretical stages 1.11 Wallis flooding factor 0.69 Heat loss on total rig (energy) 74.35 W ( 3.41 %)

Stream X-calc X-pred Flow rate (kmole/s) Reflux liquid 0.4593 1.2422e-05 Return liquid 0.7151 1.1607e-04 Feed vapor 0.6904 1.2845e-04 Bypass vapor 0.6904 4.7546e-08 Top product vapor 0.7151 1.1602e-04

Experimental and Theoretical Study of Reflux Condensation 148 Appendix G

File ’al50797.tex ’ processed at Sun Nov 2 11:14:15 1997

Data (35 data points) from files ’al50797 .raw’ and ’al50797. inn’.

Measurement Unit Mean value °95% Relative value

Tboil,l °C 51.13 7.52e-02 1.47e-03 °C 54.59 5.87e-02 1.07e-03 T L °c 53.76 6.22e-02 1.16e-03 T R °c 40.45 5.11e-02 1.26e-03 Ty °c 51.07 6.80e-02 1.33e-03 Ttest,in °c 40.31 6.83e-02 1.69e-03 Tte$t.3/4 °c 42.34 6.91e-02 1.63e-03 Tiesi,l/2 °c 43.94 6.92e-02 1.57e-03 Xses<, 1/4 °c 45.81 7.16e-02 1.56e-03 T test, out °c 47.76 7.01e-02 l,47e-03 Tcond,in °c 20.14 1.43e-02 7.10e-04 Tcond,out °c 28.67 2.95e-02 1.03e-03 Toi °c 51.16 1.01e-01 1.97e-03 To2 °c 51.80 6.83e-02 1.32e-03 Tq3 °c 51.71 6.49e-02 1.26e-03 To4 °c 52.20 6.35e-02 1.22e-03 Tos °c 49.58 7.59e-02 1.53e-03 Toe °c 51.08 6.98e-02 1.37e-03 Tot °c 48.77 7.39e-02 1.52e-03 Tos °c 49.35 6.81e-02 1.38e-03 Tog °c 45.24 6.72e-02 1.49e-03 Tio °c 49.06 6.63e-02 1.35e-03 TsuT °c 28.92 4.78e-02 1.65e-03 Vs 1/h 0.47 1.12e-01 2.38e-01 Viesi 1/h 58.92 1.83e-02 3.10e-04 Vs 1/h 8.68 6.99e-01 8.05e-02 Vy 1/h 35.69 1.18e+00 3.31e-02 P kPa 1057.92 7.36e-01 6.96e-04 W 2288.03 1.15e-02 5.03e-06

Experimental and Theoretical Study of Reflux Condensation Appendix G 149

Maximum-likelihood values: New value Old value Difference a F kmole/s 1.35e-04 1.26e-04 9.25e-06 3.19e-05 V kmole/s 1.07e-04 1.03e-04 3.97e-06 2.47e-05 L kmole/s 2.86e-05 2.34e-05 5.27e-06 1.88e-06 R kmole/s 1.07e-04 1.03e-04 3.97e-06 3.39e-06 B kmole/s 5.05e-08 5.05e-08 -3.02e-12 1.20e-08 TF K 3.28e+02 3.28e+02 4.43e-03 5.87e-02 Tv K 3.24e+02 3.24e+02 -3.72e-03 6.80e-02 TL K 3.27e+02 3.27e+02 -1.62e-03 6.22e-02 TR K 3.14e+02 3.14e+02 -7.07e-04 5.11e-02 z kmole/kmole 6.59e-01 6.65e-01 -5.81e-03 1.00e-02 y kmole/kmole 7.17e-01 7.15e-01 1.71e-03 1.00e-02 X kmole/kmole 4.44e-01 4.44e-01 -6.79e-05 1.00e-02 kmole/kmole 7.17e-01 7.15e-01 1.71e-03 1.00e-02 flfcoiZ W 2.29e+03 2.29e+03 -2.40e-06 1.15e-02 Qcond W 1.80e+03 1.80e+03 1.95e-03 6.29e+01 9test w 5.08e+02 5.08e+02 -1.95e-03 1.58e-01 flZoss w -1.89e+01 -1.89e+01 -5.82e-07 6.61e-01 P Pa 1.06e+06 1.06e+06 -4.19e+00 7.36e+02 Condenser water flow rate 181.29 mi Cooling duty on test section part 1 138.24 W Cooling duty on test section part 2 109.11 W Cooling duty on test section part 3 128.13 W Cooling duty on test section part 4 132.99 W Average heat flux 3781.58 W/m2 Number of theoretical stages 1.27 Wallis flooding factor 0.75 Heat loss on total rig (energy) -18.89 W(-0.83%)

Stream Xcalc Xpred Flow rate (kmole/s) Reflux liquid 0.4438 0.41 2.8627e-05 Return liquid 0.7171 1.0656e-04 Feed vapor 0.6592 0.66 1.3514e-04 Bypass vapor 0.6592 5.0526e-08 Top product vapor 0.7171 0.72 1.0651e-04

Experimental and Theoretical Study of Reflux Condensation 150 Appendix G

File ’b010897.tex ’ processed at Sun Nov 211:14:541997

Data (40 data points) from files ’b010897.raw ’ and ’b010897.inn\

Measurement Unit Mean value °95 % Relative value °C 49.14 8.79e-02 1.79e-03 ^boil)V °C 52.40 1.02e-01 1.94e-03 T L °C 51.75 9.73e-02 1.88e-03 TR °C 39.36 8.71e-02 2.21e-03 Ty °C 50.28 8.60e-02 1.71e-03 Ttest,in °C 41.61 5.26e-02 1.26e-03 Ttesi,3/4 °C 43.34 6.10e-02 1.41e-03 Tiest,1/2 °c 45.06 5.16e-02 1.14e-03 Tfest, 1/4 °c 46.39 5.68e-02 1.22e-03 T test,out °c 48.01 6.94e-02 1.45e-03 Tcond,in °c 18.27 1.58e-01 8.67e-03 Tcond,out °c 26.62 1.28e-01 4.80e-03 Toi °c 51.93 9.63e-02 1.85e-03 T02 °c 52.35 7.63e-02 1.46e-03 Tos °c 52.05 7.38e-02 1.42e-03 Tq4 °c 52.49 7.62e-02 1.45e-03 Tq5 °c 50.87 6.97e-02 1.37e-03 Toe °c 52.36 7.25e-02 1.38e-03 To? °c 49.77 7.02e-02 1.41e-03 Tos °c 50.71 6.51e-02 1.28e-03 Too °c 47.80 8.31e-02 1.74e-03 Tio °c 50.09 6.86e-02 1.37e-03 Tgitr °c 30.13 3.90e-02 1.30e-03 VB 1/h 0.40 9.95e-04 2.47e-03 Vtesi 1/h 40.07 1.49e-02 3.72e-04 Vb 1/h 3.53 4.78e-01 1.36e-01 V v 1/h 37.53 1.13e+00 3.00e-02 P kPa 1010.97 1.95e+00 1.93e-03 Qboil W 2383.62 7.03e+01 2.95e-02

Experimental and Theoretical Study of Reflux Condensation Appendix G 151

Maximum-likelihood values: New value Old value Difference a F kmole/s 1.30e-04 1.18e-04 1.27e-05 1.63e-05 V kmole/s 1.14e-04 1.08e-04 5.91e-06 3.25e-06 L kmole/s 1.64e-05 9.56e-06 6.83e-06 1.29e-06 R kmole/s 1.14e-04 1.08e-04 5.91e-06 3.24e-06 B kmole/s 4.17e-08 4.17e-08 5.97e-15 1.03e-10 Tf K 3.26e+02 3.26e+02 3.38e-02 1.02e-01 Ty K 3.23e+02 3.23e+02 -1.56e-02 8.60e-02 Tl K 3.25e+02 3.25e+02 -6.00e-03 9.73e-02 T R K 3.13e+02 3.13e+02 -7.75e-03 8.71e-02 z kmole/kmole 6.66e-01 6.75e-01 -9.53e-03 1.00e-02 y kmole/kmole 6.98e-01 6.96e-01 2.08e-03 1.00e-02 X kmole/kmole 4.42e-01 4.43e-01 -7.85e-04 1.00e-02 kmole/kmole 6.98e-01 6.96e-01 2.08e-03 1.00e-02 flioiZ W 2.23e+03 2.38e+03 -1.55e+02 7.03e+01 flcoraci W 1.80e+03 1.95e+03 -1.54e+02 6.84e+01

test W 2.97e+02 2.97e+02 -2.76e-03 l.lle-01 9/oss W 1.31e+02 1.32e+02 -1.216+00 6.06e+00 P Pa 1.01e+06 1.01e+06 -7.11e+01 1.95e+03 Condenser water flow rate 201.071/h Cooling duty on test section part 1 80.22 W Cooling duty on test section part 2 79.54 W Cooling duty on test section part 3 62.12 W Cooling duty on test section part 4 75.09 W Average heat flux 2208.59 W/m2 Number of theoretical stages 1.14 Wallis flooding factor 0.71 Heat loss on total rig (energy) 131.11 W( 5.88%)

Stream "%-calc X-pred Flow rate (kmole/s) Reflux liquid 0.4424 1.6388e-05 Return liquid 0.6980 1.1392e-04 Feed vapor 0.6659 1.3027e-04 Bypass vapor 0.6659 4.1730e-08 Top product vapor 0.6981 1.1388e-04

Experimental and Theoretical Study of Reflux Condensation 152 Appendix G

File ’b040897.tex’ processed at Sun Nov 2 11:14:591997

Data (15 data points) from files ’b040897.raw ’ and ’b040897.inn ’.

Measurement Unit Mean value °"95% Relative value T boii,i °C 56.10 8.63e-02 1.54e-03 T boil,v °C 60.28 2.55e-02 4.22e-04 T L °c 59.42 1.87e-02 3.15e-04 Tr °c 45.57 2.02e-02 4.44e-04 Tv °c 56.38 3.14e-02 5.57e-04 Ttest,in °c 42.11 3.03e-02 7.20e-04 Tfest,3/4 °c 44.85 3.03e-02 6.76e-04 Ttest, 1/2 °c 47.06 3.76e-02 7.99e-04 7’iest,1/4 °c 49.35 3.64e-02 7.37e-04 Ttest,out °c 52.06 3.55e-02 6.81e-04 Tcond,in °c 23.01 2.52e-02 1.09e-03 T cond^out °c 33.54 3.24e-02 9.66e-04 Toi °c 56.14 2.39e-01 4.26e-03 T02 °c 57.56 4.92e-02 8.55e-04 Tq3 °c 57.09 3.36e-02 5.89e-04 Tq4 °c 57.87 3.59e-02 6.20e-04 To5 °c 55.15 5.44e-02 9.86e-04 Tq6 °c 57.53 4.38e-02 7.62e-04 Tq7 °c 53.65 1.06e-01 1.97e-03 Tqs °c 56.24 4.72e-02 8.40e-04 Tq9 °c 49.08 3.89e-02 7.92e-04 Tio °c 54.66 3.85e-02 7.05e-04 T$ur °c 26.02 6.46e-02 2.48e-03 VB 1/h 0.45 1.82e-03 4.05e-03 Vtest 1/h 52.61 1.42e-02 2.69e-04 Vr 1/h 12.54 9.70e-01 7.74e-02 Vy 1/h 39.14 2.01 e+00 5.14e-02 P kPa 1158.01 4.34e-01 3.74e-04 Qboil W 2650.78 1.39e+00 5.23e-04

Experimental and Theoretical Study of Reflux Condensation Appendix G 153

Maximum-likelihood values: New value Old value Difference a F kmole/s 1.58e-04 1.44e-04 1.49e-05 1.34e-05 V kmole/s 1.24e-04 1.10e-04 1.34e-05 5.70e-06 L kmole/s 3.45e-05 3.31e-05 1.44e-06 2.56e-06 R kmole/s 1.24e-04 1.10e-04 1.34e-05 5.68e-06 B kmole/s 5.21e-08 5.21e-08 2.33e-14 2.11e-10 T F K 3.33e+02 3.33e+02 1.84e-04 2.55e-02 Ty K 3.30e+02 3.30e+02 4.58e-04 3.14e-02 TL K 3.33e+02 3.33e+02 -3.30e-05 1.87e-02 TR K 3.19e+02 3.19e+02 -4.03e-04 2.02e-02 z kmole/kmole 6.28e-01 6.27e-01 1.42e-03 1.00e-02 y kmole/kmole 6.87e-01 6.89e-01 -2.41e-03 1.00e-02 X kmole/kmole 4.16e-01 4.17e-01 -5.90e-04 1.00e-02 Xfl kmole/kmole 6.87e-01 6.89e-01 -2.40e-03 1.00e-02 Qboil W 2.65e+03 2.65e+03 -1.06e-01 1.39e+00 Q.cond W 1.84e+03 1.84e+03 -1.06e-01 6.44e+01 fltest W 6.07e+02 6.07e+02 1.01e-03 1.63e-01 flioss w 2.06e+02 2.06e+02 -1.32e-03 7.20e+00 P Pa 1.16e+06 1.16e+06 -2.27e+00 4.34e+02 Condenser water flow rate 150.221/h Cooling duty on test section part 1 167.31 W Cooling duty on test section part 2 134.71 W Cooling duty on test section part 3 139.45 W Cooling duty on test section part 4 165.08 W Average heat flux 4510.98 W/m2 Number of theoretical stages 1.28 Wallis flooding factor 0.81 Heat loss on total rig (energy) 205.55 W (7.75 %)

Stream X-calc X-pred Flow rate (kmole/s) Reflux liquid 0.4160 3.4526e-05 Return liquid 0.6870 1.2393e-04 Feed vapor 0.6280 1.5840e-04 Bypass vapor 0.6280 5.2072e-08 Top product vapor 0.6871 1.2387e-04

Experimental and Theoretical Study of Reflux Condensation 154 Appendix G

File ’a050897.tex ’ processed at Sun Nov 2 11:14:371997

Data (44 data points) from files ’a050897.raw ’ and ’a050897.inn\ In addition 6 serie(s) ignored due to inconsistency in data.

Measurement Unit Mean value cr95% Relative value T boii,i °C 55.47 1.12e-01 2.02e-03 T boiljV °C 59.74 1.25e-01 2.10e-03 TL °c 58.98 1.33e-01 2.25e-03 T R °c 45.38 1.44e-01 3.17e-03 Ty °c 56.21 1.31e-01 2.33e-03 Ttest,in °c 42.20 1.27e-01 3.02e-03 Ttest,3/4 °c 44.83 1.34e-01 2.99e-03 Ttest,1/2 °c 46.95 1.43e-01 3.05e-03 T test,1/4 °c 49.26 1.48e-01 3.01e-03 T test,out °c 51.89 1.62e-01 3.11e-03 Tcond,in °c 23.00 1.10e-01 4.79e-03 Tcond,out °c 33.51 1.32e-01 3.94e-03 Toi °c 56.16 1.97e-01 3.51e-03 Tq2 °c 57.48 1.53e-01 2.65e-03 Tq3 °c 57.03 1.41e-01 2.48e-03 Tq4 °c 57.84 1.39e-01 2.40e-03 Tos °c 55.12 1.41e-01 2.56e-03 Toe °c 57.70 1.43e-01 2.48e-03 Tq7 °c 53.64 1.31e-01 2.43e-03 Tos °c 56.17 1.48e-01 2.63e-03 Too °c 49.32 1.29e-01 2.62e-03 Tio °c 54.72 1.33e-01 2.44e-03 T$ur °c 24.75 8.91e-02 3.60e-03 VB 1/h 0.45 1.26e-03 2.81e-03 Ytesi 1/h 52.03 1.42e-02 2.72e-04 VB 1/h 11.74 5.28e-01 4.50e-02 Vy 1/h 39.04 1.04e+00 2.65e-02 P kPa 1148.57 2.90e+00 2.53e-03 QfcoiZ W 2623.99 1.40e+01 5.34e-03

Experimental and Theoretical Study of Reflux Condensation Appendix G 155

Maximum-likelihood values: New value Old value Difference a F kmole/s 1.55e-04 1.41e-04 1.34e-05 7.39e-06 V kmole/s 1.21e-04 1.10e-04 1.10e-05 2.94e-06 L kmole/s 3.35e-05 3.10e-05 2.43e-06 1.40e-06 R kmole/s 1.21e-04 1.10e-04 1.10e-05 2.93e-06 B kmole/s 5.17e-08 5.17e-08 3.31e-14 1.45e-10 TF K 3.33e+02 3.33e+02 2.34e-02 1.25e-01 Tv K 3.29e+02 3.29e+02 1.49e-02 1.31e-01 TL K 3.32e+02 3.32e+02 -8.63e-03 1.33e-01 TR K 3.18e+02 3.19e+02 -6.02e-02 1.44e-01 z kmole/kmole 6.24e-01 6.27e-01 -2.73e-03 1.00e-02 y kmole/kmole 6.81e-01 6.86e-01 -4.39e-03 1.00e-02 X kmole/kmole 4.17e-01 4.18e-01 -8.71e-04 1.00e-02 XR kmole/kmole 6.81e-01 6.86e-01 -4.39e-03 1.00e-02 Qboil W 2.59e+03 2.62e+03 -3.13e+01 1.40e+01 Qcond W 1.82e+03 1.85e+03 -3.10e+01 6.49e+01 fltest W 5.85e+02 5.85e+02 1.65e-03 1.59e-01 Q/oss w 1.84e+02 1.84e+02 -3.12e-01 6.52e+00 P Pa 1.15e+06 1.15e+06 -3.21e+02 2.90e+03 Condenser water flow rate 151.77 Vh Cooling duty on test section part 1 158.90 W Cooling duty on test section part 2 127.68 W Cooling duty on test section part 3 139.04 W Cooling duty on test section part 4 159.25 W Average heat flux 4349.81 W/m2 Number of theoretical stages 1.28 Wallis flooding factor 0.80 Heat loss on total rig (energy) 183.91 W( 7.09%)

Stream XcoZc Xpred Flow rate (kmole/s) Reflux liquid 0.4169 0.39 3.3451e-05 Return liquid 0.6812 - 1.2124e-04 Feed vapor 0.6240 0.62 1.5464e-04 Bypass vapor 0.6240 - 5.1681e-08 Top product vapor 0.6812 0.69 1.2119e-04

Experimental and Theoretical Study of Reflux Condensation 156 Appendix G

File 'b050897.tex' processed at Sun Nov 2 11:15:03 1997

Data (13 data points) from files ’b050897.raw ’ and ’b050897.inn ’. In addition 2 serie(s) ignored due to inconsistency in data.

Measurement Unit Mean value °95% Relative value T'boilJ °C 47.03 8.92e-02 1.90e-03 TbozljV °c 50.52 7.28e-02 1.44e-03 TL °c 50.05 7.08e-02 1.41e-03 TR °c 38.52 4.98e-02 1.29e-03 Ty °c 49.19 5.40e-02 1.10e-03 T test,in °c 42.80 2.75e-02 6.44e-04 Ttest, 3/4 °c 44.15 2.27e-02 5.15e-04 Ttest,1/2 °c 45.07 3.48e-02 7.71e-04 Ttest,1/4 °c 46.25 3.87e-02 8.37e-04 Ttest,out °c 47.58 4.02e-02 8.45e-04 Tcondjt'n °c 11.13 2.53e-02 2.27e-03 Tcond,Ottf °c 23.31 4.36e-02 1.87e-03 Toi °c 50.02 7.80e-02 1.56e-03 Tq2 °c 51.17 5.93e-02 1.16e-03 Tq3 °c 50.89 4.95e-02 9.73e-04 Tq4 °c 51.15 5.03e-02 9.83e-04 Tos °c 49.57 6.80e-02 1.37e-03 Toe °c 50.92 5.05e-02 9.92e-04 T07 °c 49.09 6.43e-02 1.31e-03 Tos °c 50.00 5.77e-02 1.15e-03 Too °c 47.00 3.86e-02 8.22e-04 Tio °c 49.56 4.11e-02 8.28e-04 Tsur °c 23.68 7.50e-02 3.17e-03 VB 1/h 0.44 1.16e-03 2.60e-03 ^test Vh 51.86 3.26e-02 6.28e-04 V r 1/h 3.84 7.05e-01 1.83e-01 Vy 1/h 45.02 9.08e-01 2.02e-02 P kPa 966.11 1.06e+00 1.09e-03 W 2452.44 2.41e+01 9.85e-03

Experimental and Theoretical Study of Reflux Condensation Appendix G 157

Maximum-likelihood values : New value Old value Difference a F kmole/s 1.43e-04 1.40e-04 3.42e-06 2.58e-05 V kmole/s 1.27e-04 1.30e-04 -2.22e-06 2.63e-06 L kmole/s 1.61e-05 1.04e-05 5.64e-06 1.92e-06 R kmole/s 1.27e-04 1.30e-04 -2.22e-06 2.61e-06 B kmole/s 4.43e-08 4.43e-08 -4.52e-15 1.15e-10 Tf K 3.24e+02 3.24e+02 7.13e-03 7.28e-02 Ty K 3.22e+02 3.22e+02 -4.81e-03 5.40e-02 TL K 3.23e+02 3.23e+02 -1.16e-03 7.08e-02 TR K 3.12e+02 3.12e+02 1.70e-03 4.98e-02 z kmole/kmole 6.49e-01 6.54e-01 -5.49e-03 1.00e-02 y kmole/kmole 6.75e-01 6.72e-01 3.74e-03 1.00e-02 X kmole/kmole 4.37e-01 4.37e-01 -1.13e-04 1.00e-02 Xfl kmole/kmole 6.75e-01 6.72e-01 3.74e-03 1.00e-02 fl&oiZ W 2.47e+03 2.45e+03 2.03e+01 2.41e+01 Qcond w 2.10e+03 2.08e+03 2.02e+01 7.27e+01 fltesi w 2.87e+02 2.87e+02 -4.26e-03 1.80e-01 9/oss w 8.96e+01 8.96e+01 4.07e-02 3.26e+00 P Pa 9.66e+05 9.66e+05 5.80e+00 1.06e+03 Condenser water flow rate 146.39 1/h Cooling duty on test section part 1 81.25 W Cooling duty on test section part 2 55.11 W Cooling duty on test section part 3 70.92 W Cooling duty on test section part 4 79.79 W Average heat flux 2134.93 W/m2 Number of theoretical stages 1.13 Wallis flooding factor 0.75 Heat loss on total rig (energy) 89.63 W ( 3.62 %) Stream xcaZc X-pred Flow rate (kmole/s) Reflux liquid 0.4371 1.6080e-05 Return liquid 0.6754 1.2737e-04 Feed vapor 0.6487 1.4341e-04 Bypass vapor 0.6487 4.4285e-08 Top product vapor 0.6754 1.2733e-04

Experimental and Theoretical Study of Reflux Condensation 158 Appendix G

File ’cl20897.tex’ processed at Sun Nov 2 11:14:43 1997

Data (50 data points) from files ’cl20897.raw ’ and ’cl20897.inn\

Measurement Unit Mean value cr95% Relative value TfcoiZ,/ °C 51.03 5.62e-02 1.106-03 Tboil,v °C 54.59 5.64e-02 1.036-03 T L °c 54.07 5.59e-02 1.03e-03 TR °c 43.94 3.54e-02 8.07e-04 Tv °c 53.17 5.04e-02 9.486-04 Tt est,in °c 45.95 1.40e-02 3.04e-04 Ttest, 3/4 °c 47.32 2.18e-02 4.60e-04 Ttest, 1/2 °c 48.23 2.336-02 4.84e-04 1/4 °c 49.60 3.32e-02 6.706-04 Ttest,out °c 50.93 4.25e-02 8.35e-04 Tcond,in °c 20.10 1.39e-02 6.936-04 Tcond,out °c 30.89 2.87e-02 9.29e-04 Toi °c 53.99 5.99e-02 1.116-03 Tq2 °c 55.01 3.50e-02 6.366-04 To3 °c 54.76 2.97e-02 5.426-04 Tq4 °c 54.79 2.10e-02 3.84e-04 To5 °c 53.23 8.09e-02 1.52e-03 Toe °c 54.80 2.25e-02 4.11e-04 T07 °c 52.80 2.63e-02 4.98e-04 Tqs °c 52.77 1.066-01 2.01e-03 Tq9 °c 51.41 4.466-02 8.676-04 Tio °c 53.11 3.79e-02 7.13e-04 Tsur °c 25.22 6.11e-02 2.42e-03 VS 1/h 0.44 9.766-04 2.21e-03 V test 1/h 39.27 4.43e-02 1.13e-03 Vs 1/h 2.84 5.18e-01 1.82e-01 Vy 1/h 59.72 4.15e-01 6.94e-03 P kPa 1217.39 3.79e-01 3.12e-04 96oi7 W 2816.34 7.29e+00 2.59e-03

Experimental and Theoretical Study of Reflux Condensation Appendix G 159

Maximum-likelihood values: New value Old value Difference a F kmole/s 1.79e-04 1.78e-04 4.11e-07 3.26e-05 V kmole/s 1.66e-04 1.71e-04 -4.88e-06 1.24e-06 L kmole/s 1.30e-05 7.71e-06 5.30e-06 1.41e-06 R kmole/s 1.66e-04 1.71e-04 -4.88e-06 1.19e-06 B kmole/s 5.48e-08 5.48e-08 -4.77e-14 1.21e-10 T F K 3.28e+02 3.28e+02 9.12e-03 5.64e-02 Tv K 3.26e+02 3.26e+02 -2.38e-02 5.04e-02 TL K 3.27e+02 3.27e+02 -1.01e-03 5.59e-02 TR K 3.17e+02 3.17e+02 1.25e-02 3.54e-02 z kmole/kmole 7.74e-01 7.66e-01 8.06e-03 1.00e-02 y kmole/kmole 7.91e-01 7.75e-01 1.57e-02 1.00e-02 X kmole/kmole 5.59e-01 5.61e-01 -1.62e-03 1.00e-02 Xfi kmole/kmole 7.91e-01 7.75e-01 1.56e-02 1.00e-02 Qboil W 2.84e+03 2.82e+03 2.23e+01 7.29e+00 Qcond W 2.54e+03 2.52e+03 2.23e+01 8.82e+01 fliest W 2.26e+02 2.26e+02 -3.81e-02 2.55e-01 flZoss w 7.01e+01 7.01e+01 1.74e-02 2.46e+00 P Pa 1.22e+06 1.22e+06 1.52e+01 3.79e+02 Condenser water flow rate 200.86 1/h Cooling duty on test section part 1 62.46 W Cooling duty on test section part 2 41.37 W Cooling duty on test section part 3 62.26 W Cooling duty on test section part 4 60.20 W Average heat flux 1682.67 W/m2 Number of theoretical stages 1.08 Wallis flooding factor 0.77 Heat loss on total rig (energy) 70.13 W (2.47 %)

Stream Xcalc Xpred Flow rate (kmole/s) Reflux liquid 0.5589 0.54 1.3009e-05 Return liquid 0.7910 1.6588e-04 Feed vapor 0.7741 0.76 1.7883e-04 Bypass vapor 0.7741 5.4767e-08 Top product vapor 0.7910 0.78 1.6583e-04

Experimental and Theoretical Study of Reflux Condensation 160 Appendix G

File ’al30897.tex ’ processed at Sun Nov 2 11:15:091997

Data (100 data points) from files ’al30897.raw ’ and ’al30897.inn\

Measurement Unit Mean value *95% Relative value T boil,l °C 50.67 3.28e-02 6.48e-04 Tboil,v °c 53.83 2.87e-02 5.33e-04 TL °c 53.17 3.51e-02 6.59e-04 T R °c 42.49 2.92e-02 6.87e-04 TV °c 51.99 3.19e-02 6.13e-04 Ttest,in °c 44.97 1.24e-02 2.76e-04 T test, 3/4 °c 46.08 1.24e-02 2.70e-04 Ttest, 1/2 °c 46.84 1.52e-02 3.24e-04 Tfest, 1/4 °c 48.24 1.78e-02 3.69e-04 T test,out °c 49.63 2.01e-02 4.06e-04 Tcond,in °c 21.24 2.73e-02 1.29e-03 Tcond,out °c 31.06 3.02e-02 9.73e-04 T0i °c 52.48 4.44e-02 8.46e-04 Tq2 °c 53.51 2.47e-02 4.61e-04 To3 °c 53.30 2.14e-02 4.01e-04 Tq4 °c 53.31 2.22e-02 4.16e-04 Tos °c 51.69 2.37e-02 4.59e-04 Toe °c 52.97 2.34e-02 4.41e-04 Tot °c 50.99 1.93e-02 3.79e-04 Tos °c 51.42 1.95e-02 3.80e-04 Tog °c 49.98 1.73e-02 3.46e-04 Tio °c 51.88 1.69e-02 3.25e-04 Tsyr °c 23.79 6.05e-02 2.54e-03 VB 1/h 0.45 9.44e-04 2.09e-03 1/h 42.26 4.40e-02 1.04e-03 Vb 1/h 3.16 3.03e-01 9.59e-02 ' Vy 1/h 44.10 4.74e-01 1.07e-02 P kPa 1182.00 7.46e-01 6.31e-04 boil W 2293.47 4.65e+00 2.03e-03

Experimental and Theoretical Study of Reflux Condensation Appendix G 161

Maximum-likelihood values: New value Old value Difference a F kmole/s 1.42e-04 1.35e-04 6.75e-06 1.31e-05 V kmole/s 1.29e-04 1.27e-04 2.34e-06 1.39e-06 L kmole/s 1.30e-05 8.61e-06 4.41e-06 8.26e-07 R kmole/s 1.29e-04 1.27e-04 2.34e-06 1.36e-06 B kmole/s 5.46e-08 5.46e-08 1.58e-14 1.14e-10 TF K 3.27e+02 3.27e+02 4.77e-03 2.87e-02 Tv K 3.25e+02 3.25e+02 -3.37e-03 3.19e-02 TL K 3.26e+02 3.26e+02 -1.01e-03 3.51e-02 T R K 3.16e+02 3.16e+02 -2.36e-03 2.92e-02 z kmole/kmole 7.56e-01 7.64e-01 -8.21e-03 1.00e-02 y kmole/kmole 7.77e-01 7.79e-01 -1.84e-03 1.00e-02 X kmole/kmole 5.50e-01 5.52e-01 -1.88e-03 1.00e-02 XR kmole/kmole 7.77e-01 7.79e-01 -1.84e-03 1.00e-02 QboiZ W 2.29e+03 2.29e+03 -3.27e+00 4.65e+00 0 cond W 1.98e+03 1.99e+03 -3.25e+00 6.96e+01 Qtest W 2.28e+02 2.28e+02 -1.52e-02 2.38e-01 flZoss W 7.71e+01 7.71e+01 -4.91e-03 2.70e+00 P Pa 1.18e+06 1.18e+06 -2.19e+01 7.46e+02 Condenser water flow rate 174.25 1/h Cooling duty on test section part 1 54.49 W Cooling duty on test section part 2 36.99 W Cooling duty on test section part 3 68.54 W Cooling duty on test section part 4 68.37 W Average heat flux 1698.55 W/m2 Number of theoretical stages 1.10 Wallis flooding factor 0.70 Heat loss on total rig (energy) 77.08 W ( 3.37 %)

Stream X-calc X-pred Flow rate (kmole/s) Reflux liquid 0.5497 1.3022e-05 Return liquid 0.7770 1.2905e-04 Feed vapor 0.7562 1.4202e-04 Bypass vapor 0.7562 5.4562e-08 Top product vapor 0.7770 1.2899e-04

Experimental and Theoretical Study of Reflux Condensation 162 Appendix G

Experimental and Theoretical Study of Reflux Condensation H Specific recommendations for future work

This appendix contains specific items for further work with dephlegmators at NTNU, and is meant as a supplement to the comments made in Chapter 9.

Theory and model The main focus of the theoretical work was developing the numerical model. Sug gestions for improvements on theoretical work are listed below.

• Include cold process stream. By including the cold process stream, the heat flux along the dephlegmator channel may be varied in a realistic manner. Multi stream capability of a PFHE is also desirable in an improved model.

• Verification of model with data from different laboratory-, pilot- and commer cial plants. Such information has not been available in this project. Verification of the model is important to obtain acknowledgment from industry.

• An extension to a multi-component mixture is desirable. This extension will ease comparison with industrial processes.

• Development of more rigid mathematical treatment of top section. The current model uses very short step lengths at the top of the dephlegmator if high purity is required. This influence computing time and stability.

• Include internal geometry of plate-fin heat exchangers.

• Use model to identify and verify new processes (C02 - recovery, VOC, LNG). Design and operation of dephlegmators on board ships with focus on vessel motion due to waves.

Laboratory

Based on the current test rig, the following improvements are suggested:

• Improve sample ports for composition measurements. The test sample loops should be designed to accommodate flushing with inert gas. The valves and the outlet from the test rig should be redesigned to avoid liquid holdup.

• All vapor and liquid lines must be equipped with valves to avoid liquid holdup during partial operation.

163 164 Appendix H

• New design of cooling circuits will improve operating stability. The low flow rates were not stable and a new design with recirculation, and better temperature control is needed. The flow passage in the cooling jacket surrounding the test section should be redesigned to stabilise the flow.

• Various problems were encountered with the instrumentation, and a revision is needed. Parallel instrumentation would have solved many problems with the flow rate measurements, both with respect to varying flow rate operating conditions, and quality control by comparison.

• Differential pressure measurements with separate pressure transmitters to avoid liquid holdup in dP-line.

• Modify measurement point for reflux liquid and feed vapor temperature to obtain “true” temperature.

• Instrumentation of test section to quantify heat flux. Install more thermocouples in refrigerant flow sections, in order to measure local temperature difference.

• Incorporate the data reconciliation method in the initial phase of new experi ments, and evaluate required accuracy of new instruments.

• Operation with ternary mixtures, and more variation of feed composition.

A new test rig may include:

• A forced circulation unit (compressor or blower) enhances flexibility on flow rates. Variation of the feed composition is easier with a forced circulation unit, where the boiler and vapor bypass may be operated individually.

• Operation with parallel channels to address flow instability.

• Operation with plate-fin passages to address flow distribution.

Experimental and Theoretical Study of Reflux Condensation