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Analysis of a high temperature fouling unit for heavy hydrocarbon fractions 2000

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ANALYSIS O F A H I G H T E M P E R A T U R E F O U L I N G U N I T F O R H E A V Y H Y D R O C A R B O N F R A C T I O N S By Martial Simard B . A . Sc., Uuiversite Laval, 1996 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF T H E REQUIREMENTS FOR T H E D E G R E E OF M A S T E R OF A P P L I E D SCIENCE in T H E FACULTY OF GRADUATE STUDIES DEPARTMENT OF CHEMICAL AND BIO-RESOURCE ENGINEERING We accept this thesis as conforming to the required standard T H E UNIVERSITY OF BRITISH COLUMBIA March 2000 © Martial Simard, 2000 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of C H EM I CAL &M6> A V ^ g g / A f c The University of British Columbia Vancouver, Canada Date Mr\GCh\ 3 f ^ __.Q0O DE-6 (2/88) Abstract W i t h the depletion and increase in the price of light crude o i l , the conversion of heavy oils and bitumens into distillable fractions in upgrading units has become an important source in meeting the demand for fuels and petrochemical products. Fouling, or the deposition of any undesirable material on heat exchangers surfaces, is a costly operational problem in conventional refineries because it increases the resistance to heat transmission and flow. The precipitation problem is worse with heavy petroleum streams because of the higher concentration of fouling precursors such as asphaltenes and polar heteroatomic species and the higher temperatures of processing required to convert the high molecular weight components. A t temperatures above 300°C, heavy oi l streams undergo thermal decomposition or free-radical reactions which lead to the formation of coke defined as toluene insoluble carbonaceous solid which fouls processing units. In order to design and operate upgrading units wi th m i n i m u m coke deposition, the chemical, thermal, and fluid mechanical factors causing the problem must be known. A research project which involved kinetic and thermal fouling studies on pi tch, gas oils, and their blends was init iated to generate such information. As part of this research, a re- circulation flow loop had been constructed to study coke deposition during flow through a vertical tube placed in an electrically heated fluidized bed. The present work was conducted to develop the apparatus, to analyze its behaviour, to evaluate the tendency of pitch-gas oils blends to form coke and to assess the capability of the unit to detect it under the appropriate conditions of bulk and surface temperatures. A series of fouling experiments was carried out by recirculating a 50:50% vol. pitch- coker heavy gas oil blend over 11-56 hour periods wi th average bulk fluid temperatures of 200-375°C, tube side velocities of 0.3-2.2 m/s (laminar flow), and average fluid bed tem- peratures in the range of 500-615° C. A number of improvements to the high-temperature unit were made to reach the desired temperature conditions, to provide the necessary measurements for adequate interpretation of results, and to increase the quality of the data. In order to determine the flow regime and to account for possible viscosity changes i i during recirculation, the density of the above mixture and the viscosity of pitch, gas oils, and their blends were measured over a wide range of temperatures. Additional tests were performed to monitor the viscosity change during recirculation of the test fluid and also the change in the amount of toluene insolubles in the 50:50% vol. pitch-heavy gas oil blend. Coke deposition was determined by mass deposition and by thermal measure- ments. Interpretation of the latter was made by use of different data analysis techniques and of empirical correlations found between process variables. Moreover, in order to see whether the absence of fouling observed was due to the fouling unit and/or to the nature of the test fluid, a blend of de-asphalted oil known to give measurable fouling rates in turbulent flow and in similar periods of time as for the coking experiments was studied. Finally, measurements of heat transfer coefficients were made in order to estimate the sensitivity of the unit to detect fouling by thermal measurements. Correlations were developed over a wide temperature range for the viscosity (80- 310°C) and density (60-145°C) prediction of any blend of pitch and gas oil. As a result, the flow regime could be determined and the viscosity drop observed in some of the runs revealed a possible bias effect on the mass flowrate measurement. Moreover, the use of different data analysis techniques and empirical equations found between process variables confirmed the liquid flowrate variations as the reason for the observed changes in the thermal resistance for the runs with the 50:50% vol. pitch-gas oil blend. The liquid flowrate variations were essentially eliminated by modifying the configuration of the bypass circuit. Also, the thermal resistance of the fluid bed was found to be as high as 38% of the total resistance, which substantially reduced the sensitivity of the unit to detect coke deposition. Finally, no significant fouling was observed both from the thermal and mass deposition measurements with the 50:50% vol. pitch-gas oil blend over the range of conditions mentioned above. As for the experiments involving a blend of de-asphalted oil, the evidence obtained was judged insufficient to draw a definite conclusion as whether sufficient fouling actually took place. in Table of Contents Abstract 1 1 List of Tables viii List of Figures x List of Symbols xiii Acknowledgement xviii 1 Introduction 1 1.1 Background 1 1.2 Fouling by Coke Deposition 1 1.3 Objectives of Work 2 2 Literature Review 3 2.1 Introduction 3 2.2 The Fouling Problem - Fundamentals 3 2.3 Fouling in The Heavy Oil Upgrading Industry 6 2.4 Classification of Fouling 8 2.5 Chemical Reaction Fouling 9 2.5.1 Thermal Decomposition 10 2.5.2 The Role of Asphaltenes in Coke Deposition 11 2.6 Effects of Process Variables 12 2.6.1 Surface and Bulk Temperatures 12 iv 2.6.2 Velocity i z 2.7 Models of Chemical Reaction Fouling 13 2.8 Experimental Techniques in Thermal Fouling 14 2.8.1 Fouling Surface Heating Techniques 15 2.8.2 Heat Transfer Coefficient in a Bubbl ing Flu id ized B e d 16 3 Character iza t ion of Feed Mater ia ls 21 3.1 Properties of Fluids 21 3.2 Density 21 3.2.1 Density of 52%wt. Pitch-48%wt. C H G O Blend 21 3.2.2 Generalization of Results 23 3.3 Viscosi ty 24 3.3.1 High Temperature Viscosity Measurements 24 3.4 Model l ing Viscosity Data 27 3.4.1 Evaluating Empi r ica l Equations 27 3.4.2 Mix tu re Viscosity Equations 32 3.4.3 Generalization of Parameters 32 4 Development and Opera t ion of the Foul ing U n i t 35 4.1 Original Apparatus 35 4.2 L iqu id Flowrate Measurement 37 4.3 Pressure Drop Measurement 37 4.3.1 Differential Pressure Transducer Design, Operation, and Calibrat ion 37 4.4 L iqu id Flowrate Est imation 38 4.5 Test Section and Fluidized Bed 38 4.5.1 A i r Distributor 39 v 4.5.2 Temperature Measurement and Control 41 4.5.3 Modifications 42 4.6 Data Collection and Loop Monitoring 42 4.7 Other Modifications and Final Apparatus 43 4.7.1 Initial Unsteady-State Period 43 4.7.2 Liquid Flowrate Fluctuations 43 4.7.3 Viscosity Reduction 44 4.7.4 Volatilization 44 5 Experimental Procedures 46 5.1 Thermal Fouling Measurements 46 5.2 Toluene Insoluble Formation and Deposition Measurements 48 6 Results and Discussion 50 6.1 Fouling Tendency of 50:50%vol. Pitch and C H G O Blend 51 6.1.1 Summary of Fouling Runs 51 6.1.2 Toluene Insolubles Measurements 53 6.1.3 Mass Deposition Measurements 57 6.2 Analysis of Variations in Liquid Flowrate 60 6.2.1 Experiments with Pressure Drop Measurement 60 6.2.2 Initial Experiments 64 6.2.3 A R M A Model and Variable Flowrate Approach 68 6.2.4 Elimination of Fluctuations 74 6.2.5 Viscosity Effect 75 6.3 Heat Transfer in a Bubbling Fluidized Bed 80 6.3.1 Heat Transfer Coefficient Around an Immersed Tube 80 vi 6.3.2 Clean Coefficient For The O i l 87 6.4 Analysis of Variations in Fluid ized Bed 90 6.4.1 Power Spectral Density 90 6.4.2 El imina t ion of Fluctuations 92 6.4.3 Sensitivity of UQ to A i r Flow Variations 96 6.5 Tests W i t h a Known Fouling F l u i d 97 7 Conclusions Sz Recommendations 103 7.1 Conclusions 103 7.2 Future Work 106 -Bibliography 108 A Calibrations 117 B Properties of Fluids and Distillation TBP curves 120 C Size Distribution of Quartz Sand Used in Fluid Bed 122 D Sample Calculations 123 D . l Tube Side Velocity, and Reynolds Number 123 D.2 Heat Flow, Overall Heat Transfer Coefficient, and Thermal Fouling Resis- tance 123 D.3 Superficial Gas Velocity, U, and M i n i m u m Fluidizat ion Velocity, Umf. . . . 124 D.4 Experimental Bed-to-Wall and O i l Side Heat Transfer Coefficients 124 D.5 Effect of h0 on Sensitivity of Uni t to detect Coke Formation 125 D.6 Calculat ion of parameters presented in Table 6.1 126 v i i List of Tables 3.1 Summary of Parameters in Equation 3.3 23 3.2 Dynamic viscosity (mPa-s)-temperature data for pi tch, C H G O , and their blends 26 3.3 Summary of Some of the Viscosity Correlations Tested 28 3.4 Constants Regressed i n the Viscosity Correlations Tested 29 3.5 Average Absolute Deviation ( A A D ) for Correlations Tested 30 3.6 Generalization of Parameters in Dutt Correlation 33 4.1 Est imat ion of Pressure Drop Across A i r Distributor 39 6.1 Summary of variables investigated i n fouling experiments wi th a 50:50%vol. blend of pitch and C H G O and with F O - H O - D A O blend ' 51 6.2 Toluene insolubles content in the in i t ia l and final test fluid for al l runs. . . 56 6.3 Coke collected in test section and equivalent l iquid thickness which would give rise to wc 57 6.4 Cross-correlation between A Tft and m at lag zero 62 6.5 Parameters regressed in Equation 6.11 for some experiments 72 6.6 Measured and calculated ini t ia l and final viscosities for Runs 17 and 18. . . 79 6.7 Predicted decreases in flowrate in Runs 17 and 18 based on two approaches. 79 6.8 Experimental and predicted ha from various methods 82 6.9 Bed-to-wall temperature difference at three axial positions (Runs 16, 20, 23). 83 6.10 Measured, and predicted h0t,nax from various correlations for Runs 16 and 20 86 6.11 Parameters involved in the calculation of /?.,- 89 v i i i 6.12 Measured (hi), and predicted (hi) coefficient from Equat ion 6.22 89 6.13 Total , and fractional tube side and shell side resistances* 89 6.14 Magnitude and period of the peaks identified in Runs 3 to 7 92 6.15 Parameters for the bandstop filters for Runs 5 and 6 94 6.16 Init ial and final values of measured and calculated variables for al l runs wi th 95% confidence interval (CI) 98 6.17 Coke collected in test section at the end of Runs 20 and 21 102 B . l Properties of pi tch and C H G O 120 B.2 Some properties of Fuel O i l , Co ld Lake Heavy O i l and De-Asphalted O i l . 120 D . l Effect of hQ on the change in 1/U0. . 125 i x List of Figures 2.1 Schematic of Thermal Resistances in a Fouled Tube 5 2.2 Schematic of Hydrocarbon Pyrolysis 10 2.3 General multistep chemical reaction fouling mechanism where A is the soluble precursor, B is insoluble foulant and C is the deposit 13 3.1 Density of mineral oi l and of 52%wt. pitch blend 22 3.2 A Typica l n-S Diagram (T = 190°C) 25 3.3 Kinemat ic viscosity-temperature data; fitted lines obtained using Dutt ' s (1990) equation and parameters given i n Table 3.4 26 3.4 Parameters &i and b2 from Mehrotra et al . (1989) and from this work. . . . 30 3.5 Kinemat ic viscosity-temperature data; fitted lines obtained wi th Equa- tions 3.9 to 3.12 34 4.1 Original Apparatus 36 4.2 Test section, fluidized bed, and air distributor 40 4.3 F i n a l Apparatus 45 6.1 Batch coking experiments of 50:50%vol. P i t ch and V i r g i n Gas O i l B lend— Expts . Yue (1998) 54 6.2 Toluene insolubles content based on actual sample weight versus recircula- tion time for al l runs (50:50%vol. pitch and C H G O blend) 55 6.3 Mass deposition measurement analysis; run number shown besides symbol. 59 6.4 Fluctuations in AT& caused by variations in mass flowrate in R u n 9 61 6.5 Relationship between A T t and rh; lines from Equations 6.6 and 6.7. . . . 61 x 6.6 Cross-correlation function between AT& and m for Runs 8 and 16 63 6.7 Linear correlation found between ATf, and m 63 6.8 Slopes of Equations 6.6 and 6.7 (lines) versus corresponding slope in indi - vidual runs (symbols) 64 6.9 Drop in ATf, in R u n 1 caused by a flowrate increase 65 6.10 Correlations found between A T i o s s , ATI,, and rh for Runs 4-11 66 6.11 Correlations observed between A 7 ) O S S and m and between A T t and ATioss. 67 6.12 Slopes of Equations 6.8 and 6.9 vs. corresponding slopes in individual runs. 67 6.13 Similar i ty of patterns in ATJ,, ATioss and ra for Runs 4, 7, and 10 69 6.14 Use of variable flowrate approach to reduce the effects of flowrate on Q; for Figure (a), a flowrate value measured at the end of the run was assumed. . 70 6.15 Relationship between the heat flow to the test section and the mass flowrate. 70 6.16 Use of variable flowrate approach to reduce the effects of flowrate on Q. . . 70 6.17 Block diagram of principle used to distinguish fouling from flowrate effects. 71 6.18 Appl ica t ion of A R M A model to predict ATb based on A P 73 6.19 Standard deviation of flowrate versus flowrate for two bypass configurations. 75 6.20 Test for correlation between A T / o s s and m for Runs 17 and 18 75 6.21 AT/oss, heat flow and mass flow measurements for Runs 17 and 18 76 6.22 Viscosity drop during recirculation of test fluid 77 6.23 Discharge coefficient vs. Reynolds number for the 1/16" diam. orifice plate. 78 6.24 Measured and predicted hQ according to different methods for R u n 20. . . . 81 6.25 Measured and predicted h0 according to Equation 2.19 for Runs 16 and 23. 81 6.26 F i t by Equations 2.19 and 2.24; data from Makhor in and Kharchenko (1964). 84 6.27 Experimental (symbols) with air at varying bed temperatures and pre- dicted h0 (Equation 2.19); reproduced from Molerus and W i r t h (1997) with permission 85 x i 6.28 Experimental and predicted h0,max (Equation 2.24) at different levels of temperature; reproduced from Molerus and W i r t h (1997) wi th permission. 85 6.29 Instantaneous h on a vertical tube; adapted from Mick ley et al.(1961). . . . 87 6.30 Samples of the periodogram obtained from the F F T (Data from R u n 5). . 91 6.31 Bode diagram of the band-stop filter used to reduce oscillations i n R u n 5. . 93 6.32 Samples of the periodogram for the raw and filtered ATb for R u n 5 94 6.33 Raw and filtered heat flow for Runs 5 and 6 95 6.34 Test revealing the effect of air pressure on air temperature, T a t r 95 6.35 Correlation between U0 and the fluid bed temperatures in R u n 20 97 6.36 Heat flow, (1/C/ G), and mass flowrate in Runs 19 to 21 101 A . l A i r rotameter calibration curve 117 A.2 Orifice 1/8" calibration and discharge coefficient 118 A . 3 Orifice 1/16" calibration and discharge coefficient 119 B . l S I M D I S T for V i r g i n and Coker H G O s 121 C. l Size distribution of quartz sand used in fluidized bed; mean particle diam- e t e r ^ . 3 4 m m 122 x i i List of Symbols A , a B, b,bi,b2 C CR D Dth dp Dv E G,g h h j K L U m m, m Am,, 71 N constants inner and outer tube surfaces, respectively constants constant (Chapter 3), discharge coefficient elsewhere heat capacity of test fluid, particles, and gas, respectively ratio of heat transfer coefficient for vertical tube to that for tube located on bed axis rate of shear (p.25) and tube diameter elsewhere diameter of orifice throat particle diameter bed internal diameter activation energy- superficial mass fluidizing velocity and gravity constant, resp. convective heat transfer coefficient predicted convective heat transfer coefficient thermal conductivity of tube wall , deposit, gas, and l iquid , resp. instrument factor length of vector (Section 6.4), length of heated tube elsewhere hydrodynamic and thermal entry lengths, respectively laminar flow length scale mass of deposit per unit heat transfer area mass flowrate, average (over time) mass flowrate change in m predicted from viscosity data change in m predicted from Eq. 6.16 test speed (Eq. 3.6), number of data points elsewhere number of data points xin p period A P pressure drop across orifice plate ^•Pdist pressure drop across air distributor A P t , A P v total pressure drop, and pressure drop across the fluid bed Q, Q heat flow, average (over time) heat flow q heat flux q~l backward shift operator R universal gas constant Rf, Rt, Rw thermal resistance (fouling, total, and tube wall, respectively) Rf thermal fouling rate ?• tube radius Tfc cross-correlation function at lag k S, s torque, and constant, respectively Sp, Sp periodogram, and power spectral density, respectively T, T temperature, and average temperature, respectively TI toluene insolubles t time index tr recirculation time A T temperature difference AT/,„, ATi,n log mean temperature difference (LMTD) , and average L M T D ATioss, ATioss temperature difference between bulk temperature of test fluid in the tank and bulk inlet temperature, and average A T / o s s U gas superficial velocity Ui, U0 overall heat transfer coefficient (based on inner and outer surfaces of tube, respectively) UOT gas velocity at air distributor nozzle V, v volatile yield, and liquid velocity, respectively w defined by Eq. 6.27 wc weight of coke in test section at the end of a run %wtp • weight percent of pitch xiv WN defined by E q . 6.24 X discrete fourier transform of sequence {xt} x tube length Xd deposit thickness Xfd,T,x/d,H thermal and hydrodynamic entrance regions Xi weight fraction of component i xp weight fraction of pitch xres equivalent l iquid thickness of residue which would give rise to wc xt time series y data z coordinate Dimensionless groups Ar Archimedes number Gz Graetz number Nu Nusselt number Pr P randt l number Re Reynolds number Greek letters P orifice-to-pipe diameter ratio e fluid bed voidage 8 frequency / i dynamic viscosity of l iquid f.ig dynamic viscosity of gas v kinematic viscosity of l iquid p density of l iquid Pd density of deposit xv pg density of gas pp density of particles pres density of residue a standard error r shear stress Subscripts 0 initial air air entering the fluid bed b bulk hot bottom of fluid bed c calculated with a constant flowrate value measured at the end of each run cb at calibration d deposit / final fb fluid bed h hot medium 1 inside (or inner) of the tube or liquid side in inlet j component j M by Molerus m mixture max maximum mf minimum fluidization conditions mid middle of fluid bed o outside (or outer) of the tube or fluid bed side out outlet p pitch .s surface xvi T at a given temperature t t ime index top top of fluid bed v calculated wi th actual flowrate value Abbreviations A A D average absolute deviation C H G O coker heavy gas oi l CI confidence interval D A O de-asphalted oil F O fuel oil H O heavy oil L H S left hand side M C R micro carbon residue (amount of solid left behind when a sample is pyrolyzed in an inert gas) R H S right hand side SS time required to get to thermal steady-state xvn Acknowledgement I would like to thank my supervisors, Dr . Pau l Watkinson and D r . E z r a K w o k , for their support, guidance, and helpful suggestions throughout my research. Special thanks must go to Dr . K . L . Pinder for his help regarding viscosity measure- ments and to Dr . D . Posarac who helped me solve several technical difficulties. Support and technical advice from the staff of Mechanical workshop, Electr ical shop, Stores, and Chemical Engineering office are truly appreciated. Also I would like to thank my colleagues Michael Chong P ing , Petar Knezevich, E m a n A l - A t a r , and Ian Rose for their friendship and assistance. The financial support of Syncrude Canada L imi ted and N S E R C are gratefully ac- knowledged. Final ly, to my family for their encouragement and love, this thesis is dedicated. xvni Chapter 1 Introduction 1.1 Background The increase iii the price of conventional crude oil and its depletion have increased the interest for exploitation of alternate sources such as the vast reserves of heavy oils and bitumens found in tar sands of Western Canada. These feedstocks contain much larger amounts of residuum—the 524° C+ fraction of a crude oil or bitumen—than conventional crude oil, and hence require more processing. The current practice consists of converting the residua, and pitch—524° C+ product from processing a crude oil or bitumen—to produce synthetic crude oil that is suitable for conventional refinery processing. Gray (1994) has provided an excellent description of the upgrading processes of heavy oils and bitumens. 1.2 Fouling by Coke Deposition Fouling can be defined as the accumulation of unwanted material at a phase interface. Fouling of heat exchanger surfaces in which organic streams are heated is the cause of important economic, penalties that have been discussed by Van Nostrand Jr. et al. (1981), by Bott (1995), and others. At temperatures above 300°C, heavy oil streams undergo thermal or free-radical reactions which lead to the formation of coke, defined as toluene- insoluble carbonaceous solid. In processing petroleum streams, coke frequently deposits on the surface of processing equipment and causes fouling. Precipitation of carbon-rich material is worse with heavy petroleum streams such as bitumen from oil sands because of the higher temperatures of processing required and the higher concentration of precursors to coke formation such as asphaltenes and polar heteroatomic species. 1 Introduction 2 1.3 Objectives of Work As heavier feedstocks are processed in upgrading and refinery units, efforts are made to know the conditions which lead to coke and deposit precursors formation and deposition. The design and operation of units with minimum deposits require an understanding of the chemical, thermal and fluid mechanical factors which govern the processes leading to solids formation. The ultimate goal of this research is to generate information on deposition processes taking place in heavy hydrocarbon streams, such as pitch and gas oil blends, through thermal fouling studies. To this end,, a re-circulation flow loop capable of reaching high surface and bulk temperatures was constructed. The objective of the present work was to develop the new fouling unit, to analyze its behaviour, and to evaluate its capability to detect coke formation in pitch-gas oil blends so that progress towards the primary goal stated above can be achieved. More specifically the objectives of this study are • To modify the fouling unit so that viscous hydrocarbon streams can be processed and such that higher bulk temperatures are achieved. • To provide additional measurements to ensure adequate monitoring and control of the unit and to facilitate the analysis of the fouling data. • To characterize pitch, heavy gas oils, and blends by measuring the density and viscosity in the temperature range of thermal fouling studies to permit the flow regime to be determined. • To perform a series of fouling experiments to test the coke detection limits in the fouling unit. • To distinguish fouling from other process variable effects, to improve the quality of the data by eliminating known effects, and to reduce variations in process variables. Chapter 2 Literature Review 2.1 Introduction The build-up of undesired material on a surface, or fouling, is a widespread problem that has been observed to occur in many applications of heat exchangers. Because the subject matter of such a universal problem is quite broad, only the issues directly relevant to the present work are briefly discussed. This literature review is intended to provide a general background to the fouling problem and covers some aspects which occur in processing heavy petroleum streams typical of the heavy oil upgrading industry. 2.2 The Fouling Problem — Fundamentals The accumulation of deposits considered here is the one occurring on the surface of a heat exchanger. In the following paragraphs, the basic equations governing the rate of heat transfer in heat exchangers will be recalled along with implications of fouling. Consider a simple double pipe heat exchanger. An energy balance around a differen- tial control volume for the flow in a tube leads to the following equations after certain assumptions are made—fluid is not undergoing a phase change, negligible potential and kinetic energy changes, constant mass flow rate, and negligible heat transfer between the exchanger and its surroundings—and integration from the tube inlet in to the outlet out (Incropera and DeWitt (1996)): dQ = m • Cp • dTt, Q = m • Cp • (Tb,oul.- Tbtin) (2.1) where the subscript b refers to mean (or bulk) temperature of the fluid at a given cross- section. The total heat flow, Q, can also be related to the heat exchanger surface area 3 Literature Review 4 and the temperature difference between the cold and the hot medium (denoted by the subscripts b and h, respectively). If an overall heat transfer coefficient U is used in place of a single convection coefficient, an extension of Newton's law of cooling is obtained, which applies to the entire tube: Q = Uo-Ao- A T / m = Ui • A, • ATlm (2.2) where AT/,,, is an appropriate log mean temperature difference to account for the axial variation of the radial temperature gradient and the subscripts i and o indicate that U can be based on either the inner (Ai — TtDiL) or outer (Aa = nD0L) tube surface area. The specific form of AT depends on the flow configuration and can be derived by applying energy balances to differential elements in the hot and cold media. For a smooth, and clean single-tube heat exchanger, the overall heat transfer coefficient is given as: U0 • A0 = Ui • A,; = 4- = -. r - (2.3) \hiAi T 2nkL lioAoJ The thermal resistance under clean conditions is therefore: » = 1 = 1 = f 1 , ^(r0/ri) 1 \ ' U0-A0 Ui-Ai \hiAi 2M h0A0) { ' } During normal heat exchanger operation, surfaces are usually subject to deposit formation and this represents an additional heat transfer resistance which increases with time. The technical problems associated with this layer are numerous and have been discussed by several authors, among them Bott (1988), but can be summarized in terms of two major effects. The thermal conductivity of the fouling layer is generally lower than the other resistances and this results in a loss of heat transfer efficiency. Also, the reduction of the flow area due to the presence of the deposit causes a blockage effect, which coupled with the usually rough surface presented by the foulant, increases the pressure drop through the heat exchanger. This layer can be accounted for by introducing a fouling resistance, Rj. If we now consider deposit formation only on the inside surface of the tube, then the increase in Literature Review 5 fouling resistance inside the tube over time t can be described as: _ xj{t)_ = m(i) ^ 6^ where m is mass deposited per unit heat transfer area, pj is deposit density, and kj is deposit thermal conductivity. Equation 2.6 is valid only for thin deposits. This situation is illustrated in Figure 2.1 which also shows the various thermal resistances acting in series. In addition, the initial fouling rate is an important parameter in thermal fouling studies and is given by: The two special cases of interest in heat transfer—constant hot fluid temperature and constant surface heat flux-—have some important implications on fouling. The former is Tb l^h. Rf/Ai Rw l/Aoho Th • — V W — \ A A H W W W V — • Figure 2.1: Schematic of Thermal Resistances in a Fouled Tube. Literature Review 6 closely approximated, for example, when the surface is in contact with a freezing liquid or a condensing vapor while the latter may be realized from an electric heater. If we consider a local heat transfer at any axial position z, the heat flux may be obtained from Equation 2.2 where AT/, n simplifies to yield: q(z, 0) = U0(z, Q)[Th{z, 0) - Tb(z, 0)] (2.8) At time t we have by making use of Equation 2.5: = ! , j D , TsPU*,*) - Tb(z,t)} (2.9) Uo(z,0) "I" Ai Kf,'\Z'T> For constant local T/,, as i?/)t- increases, the local heat flux decreases over time. Provided that T/t is constant over time, the total heat flux will decrease whether or not the hot fluid temperature is uniform over the surface. If T), is also uniform over the surface and the surface temperature is an important factor determining fouling, the measured initial fouling rate is expected to apply to the whole tube. However, when constant hot fluid temperature conditions prevail, the deposit/fluid interface temperature decreases as the surface fouls. Equations 2.8 and 2.9 also reveal that to maintain a constant local heat flux implies that the local hot fluid temperature must be increased as i?/jt- increases: Uo(z,0)[Tk{z,0) -rt(z,0)] - i X L , ATh{z,t)-Tb(z,t)] (2.10) Uo(zfl) + Ai KfAZ^) If the heat flux is also uniform over the surface, it can be shown (Incropera and DeWitt (1996)) that the mean temperature Tb varies linearly between Tbtin and TbyOUt\ the variation of the mean temperature along the tube may also be obtained if q is a known function of the distance. Note that a uniform heat flux implies that the surface temperature varies along the tube. Furthermore, in the case of a thin and hydrodynamically smooth deposit, the local deposit/fluid interface temperature remains constant at the clean wall temperature value as the surface fouls. 2.3 Fouling in The Heavy Oil Upgrading Industry Heavy oils and bitumens are solid and semi-solid petroleum materials consisting of high molecular weight hydrocarbons, and contain large quantities of residuum which is defined Literature Review 7 as material boiling above 524°C. The conversion of heavy oil residua to distillates (C 5+ to 524°C-) is of particular importance in Canada because of the vast bitumen reserves in Western Canada. These feedstocks are considerably heavier and more difficult to process than traditional crudes; the current practice consists of converting the residua and pitch to produce synthetic crude oil that is suitable for conventional refinery treatment. Primary upgrading followed by hydrotreating are the two stages in which residua are upgraded, as explained by Gray (1994). Primary upgrading requires breakage of the carbon-carbon bonds in the residua and there are two approaches for doing this: hydrocracking and thermal processes. In the latter, the residuum is heated in an inert atmosphere and carbon in the form of coke, is rejected. Thermal-cracking processes are commonly used commercially to convert residua into distillable liquid products. Example processes include visbreaking, delayed coking and fluid coking. Within the coking units, coke formation is desired and promoted, leaving a lighter liquid as gaseous products. The coke is recovered as a by-product. When bitumen is processed under the severe temperature conditions of these thermal processes, there is usually a tendency for coke formation outside the units as well, and this can lead to technical difficulties. Fouling of processing equipment and heat exchanger surfaces by coke deposition is especially severe during the upgrading of heavy oils because of the higher temperatures of processing. These deposits must ultimately be removed from the equipment and disposed of. The processing of heavy oils with minimum deposit formation hinges on understand- ing the reaction fundamentals of the heavy ends and the thermal and fluid mechanical factors which govern the process. However, hydrocarbon processing deals with undefined mixtures. Trace metal contaminants, heteroatoms (S, N , 0 containing species), short- lived radicals, catalytic, effects and the large number of components combine to make the chemistry involved in this type of fouling exceedingly complex (Watkinson (1992)). The complicated nature of fouling chemistry in turn affects the thermal and physical processes involved. In the remaining sections, some of the literature dealing with the key factors involved in the chemical and physical processes which lead to solid formation will be briefly reviewed. Literature Review 8 Experimental techniques that have been used in previous thermal fouling studies will also be described. Finally, principles and correlations for heat transfer in a bubbling fluidized bed will be discussed, since a fluid bed unit was used in the current work. 2.4 Classification of Fouling In order to facilitate analysis of fouling and to provide a conceptual framework for sys- tematic research, Epstein (1983) has classified fouling into five primary categories. Crys- tallization fouling includes precipitation and solidification fouling. The former is due to formation of crystals from dissolved substances on the surface while the latter refers to the freezing of the process fluid—or constituents—onto a subcooled surface. Particulate fouling is the accumulation of suspended solids from the fluid stream on a surface. Deposit formation at the heat transfer surface resulting from chemical reactions in the flowing fluid in which the wall is not a reactant has been called chemical reaction fouling. Corrosion fouling occurs when the wall is involved in the formation of indigenous corrosion products on the surface. Biofouliug was another category defined which accounts for the deposition and growth of organisms on a heat transfer surface. Epstein (1983) also proposed a general sequence of events which may play a role in all of the above fouling types: 1. Initiation 2. Transport of foulant 3. Attachment to the surface 4. Removal of the deposit 5. Aging of the deposit on the surface The deposits resulting from organic fluid fouling are usually strong such that no removal processes are significant (Watkinson (1992)). On the other hand, aging of deposits is particularly important (Watkinson and Wilson (1997)). Literature Review 9 This classification should be used with care since it is not likely that practical heat exchanger fouling is due to only one type. Most fouling problems are the result of combi- nations and interactions of factors which belong to more than one of the above categories. This was pointed out by Murphy and Campbell (1992) who discussed fouling in refin- ery heat exchangers under seven categories, of which the following four—inorganic salts, sediments, filterable solids, and corrosion products—arise from impurities. Three others— oxidative polymerization, asphaltene precipitation, and coke formation—arise from chem- ical reactions of constituents of the oil. Nevertheless, fouling in organic fluids is generally regarded as belonging primarily to chemical reaction fouling, but may be intrinsically related to other categories. 2.5 Chemical Reaction Fouling Chemical reaction fouling was defined by Watkinson (1988) as a deposition process in which a chemical reaction either forms the deposit directly on a surface or is involved in forming precursors (or foulants) which subsequently become deposited. Unlike corrosion fouling, reaction does not take place with the wall itself. Reviews of chemical reaction foul- ing by organic fluids include those by Watkinson—Watkinson (1988), Watkinson (1992), Watkinson and Wilson (1997)—, by Crittenden (1988), and by Bott (1995). Watkinson (1988) attributed chemical reaction fouling for organic fluids to three gen- eral classes of reactions: autoxidation, polymerization, and thermal decomposition. Other terms for thermal decomposition include thermolysis, pyrolysis, cracking, etc. A final polymerization step to form iusolubles occurs in both autoxidation and thermal decom- position and, when precursors are already present, iusolubles can be directly formed by polymerization. Although these reaction classes overlap in many fouling problems, at tem- peratures typical of thermal processes (i.e. T> 350°C), thermal decomposition becomes the predominant route in the production of fouling precursors. Literature Review 10 2.5.1 Thermal Decomposition Since coke formation from pitch and residuum involves the liquid phase and the gas phase, it is important to consider the reactions that can occur in both phases. Reviews of carbon deposition from gas-phase pyrolysis have been given by Oblad et al. (1979) and by Albright et al. (1983). Coke, is formed from light feedstocks such as methane, ethane, propylene, butadiene or medium cuts such as naphthas, which are pyrolyzed at temperatures over 700° C. The gas phase reactions result in formation of aromatics which then react to produce coke. The kinetics of possible thermal reactions of olefins has been reviewed by Albright et al. (1983) and by Sakai (1983). These systems are also discussed by Froment (1981) in his review of chemical reaction fouling. More recent information includes the works by Kumar and Kunzru (1987), Kopinke et al. (1993), and Huntrods et al. (1989). Also a survey of recent work in the light hydrocarbon pyrolysis area has been given by Bach et al. (1995) in which additional mechanisms for deposit formation in transfer line exchangers are given. Pyrolysis reactions in the liquid phase occur from temperatures below 300-350° C on upwards. Accumulation of high molar mass species on heat transfer surfaces may be the result of degradation reactions followed by synthesis of high molecular weight compounds. Synthesis reactions include cyclization, aromatization and ring condensation. These ob- servations have been described by Fitzer et al. (1971) in an extensive, review of pyrolytic conversion of organic compounds related primarily to carbon or coke formation. Their schematic for the conversion of organic compounds to carbonaceous solids can be summa- rized as shown in Figure 2.2. The same authors pointed out that unsubstituted aromatics H y d r o c a r b o n D e h y d r o g e n a t i o n C r a c k i n g _ A r o m a t i c s Deal ky l a t ion P o l y c y c l i c aromat ics Heavy res idues Semi c o k e ^ C o k e M i x t u r e u ^ C y c l i z a t i o n C y c l i c Res idues P o l y c o n d e n s a t i o n Figure 2.2: Schematic of Hydrocarbon Pyrolysis. react by chemical condensation to produce polynuclear aromatics; anthracene was found very active as was also reported by Madison and Roberts (1958). These thermal decom- Literature Review 11 position reactions proceed via free radical mechanisms and have also been discussed by Lewis (1980) who emphasizes thermal polymerization reactions for polynuclear aromatics. 2.5.2 The Role of Asphaltenes in Coke Deposition Since petroleum residua are. complex mixtures of thousands of compounds, the identifi- cation of specific fouling precursors involved in the reactions leading to coke deposition is not possible. For that matter, a common approach has been to separate residua and their reaction products into pseudocomponents by the use of solvents and then to identify the pathway for chemical change by the conversion of each pseudocomponent into others. One such pseudocomponent is the asphaltenes that are soluble in aromatic solvents (e.g. benzene, toluene) and insoluble in paraffinic solvents (e.g. u-pentane, n-heptane) and are high-molecular weight substances. Strausz et al. (1992) proposed a structure for asphal- tene which was consistent with recent research and reported aromatic clusters with side chains and heteroatoms in its structure. The predominant role of asphaltenes in crude oil fouling under nonoxidative conditions has been claimed by several authors including Murphy and Campbell (1992), Eaton and Lux (1984) and Dickakian and Seay (1988), although confusion remains about the role of the physical and chemical processes involved. Mechanisms for deposit formation by asphaltenes have also been given by Dickakian and Seay (1988), Eaton and Lux (1984) and by Lambourn and Durrieu (1983). The residuum processing literature suggests some approaches for dealing with fouling and coke formation in processes such as those described in Section 2.3 (see e.g. Lott et al. (1996)). The thermal reactions of asphaltenes leading to coke formation under conditions typical of these processes have been discussed by many authors including Speight (1991), Trimm (1983), Lott et al. (1996) and have been recently reviewed by Asomaniug (1997). Furthermore, an important model of residuum thermolysis based on asphaltene solubility and phase behaviour has been developed by Wielie (1993). Literature Review 12 2.6 Effects of Process Variables 2.6.1 Surface and Bulk Temperatures The effect of surface temperature is certainly a cri t ical factor in deposition processes which are chemically controlled and has been reviewed by Watkinson and Wi l son (1997), Bot t (1995), Crit tenden (1988), and others. Since there may be several reactions leading to coke deposition, and given that selectivity may be a strong function of temperature, a simple dependence of fouling rate on temperature is not always exhibited. Nevertheless, several investigations—see e.g. Watkinson and Epstein (1969), Vranos et al . (1981), Braun (1977), Crit tenden et al . (1987), Taylor (1969)—have shown that the in i t ia l fouling data can be correlated by an Arrhenius-type equation, i.e. ^ ( O ) a e x p ^ j (2.11) where Ts is the surface temperature. Watkinson (1988) provides a summary of published activation energies. The role of bulk temperature for fouling i n which chemical reactions are involved must also be investigated. However, where bulk temperature effects have been studied, its effect, as opposed to that of wall temperature, has not been clarified as mentioned by Watkinson (1992). 2.6.2 Velocity The effects of velocity on organic fouling at a fixed wall temperature are contradictory as described by Bot t (1995), Watkinson (1992), and Crittenden (1988). It is generally accepted that the problem of hydrocarbon fouling can be reduced to some extent by the use of higher velocities and this idea is reinforced by T E M A (1978), which gives design fouling resistances that conform to this trend. However, many investigations discussed in the preceding articles—see e.g. Vranos et al . (1981), Crit tenden et al . (1987)—do not agree wi th this result. This confusion may be attributed to the effects of velocity on heat and mass transfer which complicate the analysis to find the dominant effect. For example, if the fouling rate is solely controlled by a chemical reaction, then enhanced mass transfer Literature Review 13 to the surface as a result of increasing the velocity will not change the situation. As well, increasing the velocity may reduce the wall temperature through the heat transfer coefficient thereby affecting the reaction kinetics of the deposition process. On the other hand, if the fouling process is mass-transfer controlled, an increase in velocity will result in an improved mass transfer, thereby promoting the deposition process. 2.7 Models of Chemical Reaction Fouling As was shown in Sections 2.5 and 2.6, chemical reaction fouling is explained through chemistry and operating variables effects. As a result, understanding of chemical reaction fouling may require (Watkinson and Wilson (1997)): 1. Identification of the reactants and precursors; 2. Determination of the kinetics of reactions that form precursors; and 3. Determination of whether the solid fouling phase is initially formed in the bulk, in the thermal boundary layer, or on the heated surface. A general multistep chemical reaction fouling model that can take into account the chemi- cal and physical processes involved has been proposed by Watkinson and Wilson (1997)— see also Watkinson and Panchal (1993)-—and is reproduced in Figure 2.3. Based on this Figure 2.3: General multistep chemical reaction fouling mechanism where A is the soluble precursor, B is insoluble foulant and C is the deposit. Literature Review 14 model, they have described several pathways leading to deposit formation. The cri t ical issues discussed in the literature associated wi th modeling chemical reaction fouling and in this paper in particular, are bulk reaction versus surface reaction and adhesion or at- tachment versus mass transfer. This model has been used to visualize different controlling mechanisms. 2.8 Experimental Techniques in Thermal Fouling According to Equations 2.5 and 2.6, we may measure fouling by thermal resistance Rf, deposit thickness, xj, or mass per unit heat transfer area, m. Thermal fouling studies refer to cases i n which the thermal fouling resistance is the primary response measured whereas i n mass deposition studies, the fouling deposit is weighed. The experimental techniques used in fouling studies have been reviewed by Braun and Hausler (1976), subsequently by Knudsen (1981) and Fetissoff (1982), and more recently by Bot t (1995). Thermal fouling resistances may be obtained from laboratory studies and from plant data. In-plant measurements are useful but do not usually lend themselves to the degree of control necessary for acquiring reliable fouling data. M u c h of the literature associated wi th fouling of heat exchangers is based on laboratory work. However, laboratory data have also important shortcomings which have been discussed by Bot t (1995). Because fouling in refinery exchangers can take weeks or months to reach significant levels, it is common practice in the laboratory to modify one or more of the operating parameters so that an accelerated test lasting only hours or days can be achieved. Thus, processes which may occur in industrial exchangers over periods of months are measured under more severe conditions over periods of days or weeks. The uncertainties introduced by using such an apjDroach are undoubtedly worse in chemical reaction fouling than in the other types of fouling, since the nature of the reactions occurring and the selectivity to certain reaction products may be a strong function of conditions as stated by Watkinson (1988). Furthermore, in laboratory thermal fouling studies, recirculation of the process l iquid is generally employed in order to use reasonable quantities of fluid. Recycle of the fluid across a simulated heat exchanger surface that is at a raised temperature may bring about permanent chemical changes in the fluid so that the fluid is no longer representative of Literature Review 15 the process fluid. This phenomenon is particularly acute where chemical reaction fouling occurs. Despite these concerns however and given the generally poor state of knowledge in chemical reaction fouling from residua, laboratory investigations can provide insights into fouling mechanisms and as such, give valuable data that may be useful in formulating models of fouling. It is also possible to study the effects of velocity and temperature on the fouling process that w i l l be invaluable in the design and operation of full scale heat exchangers. 2.8.1 Fouling Surface Heating Techniques Numerous methods for heating a fouling surface have been used in the past and have been discussed and described by Fetissoff (1982) and by others. However, none of them were suitable for reaching the high surface temperatures required for the present study. To address this issue, other kinds of devices were considered. When the fouling process occurs inside a tube and is measured v ia an overall heat transfer coefficient, say U0, representing several resistances in series (see Equat ion 2.4), it is crucial that UQ be sensitive to /i,- in order to detect fouling. If the other resistances are large compared to the resistance inside the tube, the measurement of UQ w i l l be insensitive to fouling inside. The fluidized bed was selected for the heating method because of the high temperature it can reach and of its well-known temperature uniformity that exists in both the radial and axial directions. Heat transfer coefficients in gas fluidized beds have been found to be considerably higher than in single-phase gas flow i n an empty tube (see Gelperin and Einstein (1971)). Hence the fouling unit consisted of a vertical tube in a heated fluidized bed. The heavy oil flowed in the tube, and the bed was fluidized with air. A quantitative value of the heat transfer coefficient between surface and bed is often required when dealing with fluidized beds—for example in estimating the surface tem- perature or the relative importance of the resistances involved as discussed above. In the present work, three tests were performed in which wall temperature measurements were obtained for this matter. In the following paragraphs, some calculation procedures for hQ Literature Review 16 (see Equation 2.4) that have been reported i n the literature and which are applicable to the fouling unit w i l l be given and briefly discussed. It should be noted that these correla- tions are far from universal and most are l imi ted to a narrow range of conditions because of the complex nature of fluidized contacting. Also, their predictions usually differ widely as stated by Grace (1982) who mentioned that the accuracy of several correlations should not be assumed to be better than ± 5 0 % within their ranges of application. Because the present work does not focus on heat transfer in a fluidized bed, a general background relevant to the system used is outside the scope of this thesis. A good summary of the principles involved wi th several references can be found i n K u n i i and Levenspiel (1991). 2.8.2 Heat Transfer Coefficient in a Bubbling Fluidized Bed The hydrodynamic and thermal behavior of fluidized beds are commonly characterized by the powder classification scheme proposed by Geldart (1973) or by that of Saxena and Ganzha (1984), which is based on the Archimedes number defined by: Ar = { 9 r P 9 ) (2-12) where g is the gravity constant and pg and pg are the gas density and viscosity respectively. The sand used in the fouling unit belongs to Group B of Geldart 's scheme which comprises particles of mean diameter, dp, and density, pp, ly ing in the range of 40 p < dp <500 / i m , and 1400 k g / m 3 < pp < 4000 k g / m 3 . Under the conditions studied i n the present work, the sand used belongs to group I powders of Saxena and Ganzha (1984), which are defined by 3.55 < A r < 21700. Numerous empirical and semiempirical formulae have been proposed for calculating heat transfer coefficients and they can be classified into two groups, one of which relates to the determination of the max imum heat transfer coefficient, h m a x , and the other to the dependence of h on fluid velocity. Because of the shortcomings of these equations, a number of models have been developed to explain the mechanism of heat transfer in fluidized beds. The calculation procedures given below were selected based on their validity with the system used, which was characterized according to the above schemes, and on the availability of the parameters required in the equations. Previous reviews of Literature Review 17 heat transfer in fluidized beds have been given by Gelperin and Einstein (1971), Grace (1982), Xavier and Davidson (1985), Baskakov (1985), and more recently by Saxena (1989). Theoretical Studies From his review, Saxena (1989) observed that the heat transfer rate from an immersed surface in a gas-fluidized bed depends upon a number of factors, such as the size, size range, shape, and properties of the bed particles; operating conditions, namely, temper- ature, pressure, fluidizing velocity, and properties of the gas; shape, size, surface finish, and orientation of the heat transfer surface; the relative size of the heat transfer surface and the fluidized bed; and on the design of the gas distributor plate. Many models have been proposed to explain the mechanism of heat transfer (see e.g. Mickley and Fairbanks (1955), Bock and Molerus (1983), Martin (1984), etc.). However, the majority of them could not be applied to our system due to a lack of data required in the computations. The model developed by Kunii and Levenspiel (1991) was selected because it was general enough to account for many of the above factors and because of the availability of the information required. They developed a general expression for the heat transfer coefficient between a bub- bling fluidized bed and an exchanger surface. The expression accounts for the fact that part of the time the surface is bathed by gas and part of the time by emulsion packets: h = (^bubble at surface) ' $w H" {h e m u l s i o n a( surface) ' (1 (2.13) where Sw is the volume fraction of bubbles in the vicinity of the surface, and is equal to the time that the surface is bathed by bubbles. The bubble term represents the contributions of convection and radiation from the gas: . hbubble present = (hr + hg) (2.14) When the emulsion packet is present on the surface, the heat transfer occurs in series—at the wall region followed by transfer at the emulsion packet. In addition, both convection Literature Review 18 and radiation occur throughout the wall region. Combining al l of the above terms yields: h = [Sw • (hr + hg)]bubble at surface + + 1 hpacket (2.15) emulsion at surface This model has been applied wi th success for both horizontal and vertical tubes (see K u n i i and Levenspiel (1991) for more details about the different terms of Equat ion 2.15). Empirical and Semiempirical Correlations The theories and mechanisms that have been proposed, such as the one outlined above, show the general features of bed-to-surface heat transfer i n gas-fluidized beds and the importance of different variables. However, despite the elaboration of a number of mech- anistic models, empirical and semiempirical correlations are s t i l l the most common means for predicting heat transfer rates (Grace (1982)). Experts i n the field (see e.g. Bot ter i l l and Hawkes (1989)) prefer empirical equations such as the one given by Zabrodsky et al . (1976). The heat transfer coefficient for an immersed surface i n a gas-fluidized bed of systems belonging to groups I and I IA wi l l depend upon the orientation of the surface wi th the flow of gas i n the fluidized bed (Saxena (1989)). Experimental investigations of h for vertical tubes are relatively more scarce than for horizontal tubes, as reviewed by Saxena (1989). One of the best-known correlation for heat transfer to a single vertical unfinned tube positioned on the axis of a cyl indrical column is that due to Vreedenburg (1960), who obtained: h(Dv-D0)(D0 d 1/3 0.105 x 10 -3 G(DV - D0) (2.16) kg \Dv(Dv-D0)figcgJ \p9(dpg)^2 where Dv is the bed diameter, kg is the gas thermal conductivity, and cg is the gas heat capacity. This equation is valid for (G dp pp/pg p,g) > 2.5 X 10 3 and G(DV — D0)/pg df2 gx>2 < 1070. According to a review of Saxena (1989), the correlations by Vreedenburg (I960) reproduced the available experimental data wi th in ± 1 0 0 % . However, these do not predict a maximum in the plot of h versus superficial mass fluidizing velocity, G , as was found in the experiments. Literature Review 19 Borodulya et al . (1980) reported h data for an 18-mm vertical heat transfer probe immersed in a 45-cm deep and 10.5-cm diameter fluidized beds of quartz sand (d p =126- 1220 ixm. They proposed: Nup = 0.96 Re0-71 Pr 0.31 (2.17) for Re < 20. The agreement of experimental data of Verma and Saxena (1983) wi th the predictions of Equat ion 2.17 was considered inadequate. The following dimensionless correlation given by Wender and Cooper (1958) has also been widely used: h oL 0.43 = 3.5 x 1 0 - 4 C , si\ 0.23 / \ 0.8 / \ 0.66 d„G\ (cv\ f pp kg(l - C) \Cg Pg J \ / W K^J \pgj for 0.01 < (dp G/p,g) < 100. In Equation 2.18, CR is a correction factor and is unity if tube is in the center of the fluid bed, e is the bed voidage, and cp is the particle heat capacity. A n average deviation of ± 2 0 % was found for the 323 data points used to develop this expression. Saxena (1989) found that this correlation reproduced their data best and was recommended as being about the best. The following recent correlation to predict h has been given by Molerus et al . (1995) in the intermediate range of 10 2 < Ar < 10 5: hh kn 0.125(1 - emf) 11 + 33.3 { ] ^ ( ^ 3 ( U - Umf) - l u, m / u-um, ll = +0.165 P ? - 1 / 3 Pg PP - Pg 2/3 1/3 1 + 0.05 U-Umf u, mf -1 (2.19) .9°*(J>P-Pg)\ where U is the gas superficial velocity and the subscript mf denotes m i n i m u m fluidization conditions. The correctness of the prediction was tested by comparison wi th more than 20 measurements covering a relatively wide range of system data and operational conditions. The accuracy of the deduced correlation was judged excellent. Literature Review 20 Maximum Heat Transfer Coefficient The correlation of Zabrodsky et al . (1976) covers a relatively broad range of data, in- cluding beds operated at high temperature and may be applied for vertical or horizontal tubes or for transfer to the external wal l : N U m a x =  h ™ * d " = 0.88 A r 0 - 2 1 3 10 2 < Ar < 2 x 10 5 (2.20) Kg A similar correlation has also been given previously by Varygin and Martyushin (1959): Numax = k m a x d p = 0.86 Ar02 30 < Ar < 1.35 x 10 5 (2.21) Kg The following correlations have also been given to predict experimental data: • Grewal and Saxena (1981): Numax = 0.9 (0.0127 Ar/D0)°-21(cp/cg)0-2 75 < Ar < 2 x 10 4 (2.22) • Denloye and Bot ter i l l (1978): Numax = 0.843 Ar0-1* + 0.86 Ar°-39d°p5 10 3 < Ar < 2 x 10 6 (2.23) • Molerus and Mat tmann (1992): Numax = r- + 0.146 (Ar P r ) 1 / 3 10 2 < Ar < 2 x 10 5 (2.24) Mathur et al . (1986) have compared some of the above correlations wi th experimental data of 13 different workers comprising 86 data points and a brief summary of their comments is given in Saxena (1989). The percentage deviations between experimental and predicted values, based on the correlation of Zabrodsky et al . (1976), range between the limits of -34.5% and 59.6% with a root-mean-square deviation of 25.1%. Equat ion 2.20 predicts 90% of the data points wi th in ± 3 5 % . O n the other hand, most of the 86 data points were underpredicted by the correlation of Varygin and Martyushin (1959). The deviations range between -46.9% and 12.6% with a root-mean-square of 19.4%. The correlation of Denloye and Bot ter i l l (1978) was also found to underpredict all the data points; the deviations were about -10% to -55%. Final ly , comparison of 61 experimental points with prediction by Molerus and Mat tmann (1992) suggested that an excellent estimate can be expected from Equation 2.24. Chapter 3 Characterization of Feed Materials 3.1 Properties of Fluids The deposition of coke-like materials was studied by recirculating through the fouling unit a blend of pi tch and coker heavy gas oi l (52%wt. pitch-48%wt. C H G O or 50:50%vol. under ambient conditions). These fluids were supplied by Syncrude Canada L t d . and are typical of the streams associated wi th their coking units. Some characteristics of these fluids provided by Syncrude L t d . are given in Table B . l . The high temperature simulated distil lation T B P curve for coker heavy gas oil is given in Figure B . l . Note that whenever the term '52%wt. pitch mixture ' is used, the balance is C H G O . Other tests were done wi th a blend of fuel oi l (75%wt. F O ) , Cold Lake heavy oi l (10%wt. H O ) , and de-asphalted oi l (15%wt. D A O ) to evaluate the capability of the unit to detect fouling by thermal measurement. This blend was chosen because of the high fouling rates measured when recirculated in another fouling unit. The composition and properties of these fluids are reported i n Table B . 2 . 3.2 Density Density is a fundamental physical property used to characterize bi tumen and is required as an input in many process calculations. In this section, the density measurements on the 52%wt. pi tch blend are presented. Also , density-temperature equations are derived to model the variation of density wi th temperature for other blends of pi tch and C H G O . 3.2.1 Density of 52%wt. Pitch-48%wt. C H G O Blend Several standardized procedures issued by the American Society for Testing and Materials can be used for determining the density of bituminous materials (Lu (1989)). The density 21 Characterization of Feed Materials 22 of the 52%wt. pi tch blend was measured by use of a pycnometer according to the standard designated as A S T M D70 using a constant-temperature bath Mode l 1130-2 from V W R Scientific which was filled wi th mineral o i l . In this method, due to the high viscosity of the materials involved, the pycnometer is partially filled wi th the mixture and water is normally added to fill it completely. For this work, since densities at temperatures higher than 100° C were desired, a mineral oi l from Fischer Co. (same as in the constant- temperature bath) for use up to 176°C was used instead of water for a l l the density measurements. The pycnometer was first calibrated wi th water in a water bath at several temperatures up to 89° C and a constant volume of 27.560 c m 3 was found. The densities of mineral oi l and of the 52%wt. pitch mixture were measured between 60 and 145°C and the following linear relationships were fitted: PT,m.oii = 866.7 - 0.621 • T PT,52% = 1042.4 - 0.621 • T (3.1) (3.2) The results are shown in Figure 3.1 with the fitted lines. Density of 52:48 wt% Pitch-CHGO Blend versus Temperature. 1020 CO E £ 980 co J 960 940 i 840 ;800 w c CD Q 760 60 70 80 90 100 110 120 130 Temperature, C 140 ) l 1 • 1 ) l ~ 7 T T - 7 - r . — _ i 60 70 80 90 100 110 120 130 140 150 Density of Mineral Oil versus Temperature. I ' i I ) - 1 i i 150 Figure 3.1: Density of mineral oi l and of 52%wt. pitch blend. Characterization of Feed Materials 23 3.2.2 Generalization of Results The data of Bulkowski and P r i l l (1978) on four Athabasca bitumen samples wi th different treatment histories in the 0 to 150°C temperature range were reported by L u (1989). They developed the following linear relationship between temperature and density: PTJ = P T ' j - A-T (3.3) In this equation, pr and pr° refer to the densities in k g / m 3 at temperatures T and T° ( = 0 ° C ) respectively. The constant A was assigned a value of 0.62 ° C _ 1 , which is the same as the constant derived from our measurements (see Equat ion 3.2). Furthermore, the densities measured by Polikar (1980)—as reported by L u (1989)—in the temperature range 0°C to 260° C for bi tumen extracted from high-grade Athabasca oi l sands can also be represented by Equation 3.3 with A=0.62 ° C - 1 . Based on these findings, a value of A of 0 . 6 2 ° C _ 1 was assumed for any blend of pitch and C H G O . The intercepts for pitch and C H G O , PT",pitch and PT°,CHGO, were found based on the knowledge of their densities at 25°C. The parameters are summarized in Table 3.1 for pitch, C H G O , 52% wt. pitch blend, mineral o i l from this work and Athabasca bitumen from Bulkowski and P r i l l (1978). The 95% confidence interval is given for the 52%wt. pitch mixture and for mineral o i l . The densities of any blend of pitch and C H G O at a given temperature can then be estimated from the following mixing rule using Equation 3.3 for component densities: PT,,n = xp • P T , P + (1 - Xp) • PT,CHGO (3.4) For the 52%wt. pi tch mixture, the deviation between the predicted and the measured densities is 1% over the temperature range 60-145°C. Table 3.1: Summary of Parameters in Equation 3.3 Fluid p T o (kg/m 3) A ("cr 1) Source Pitch 1086.8 0.62 Syncrude CHGO 975.0 0.62 Syncrude 52%wt. pitch 1042.4±0.6 0.621±0.005 Present work Mineral Oil 866.7±1.4 0.62±0.01 Present work Athabasca 1025 0.62 Lu (1989) Characterization of Feed Materials 24 3.3 Viscosity Viscosity is the property of a fluid that measures resistance to movement of adjacent fluid layers (Miadonye and Puttagunta (1996)). For Newtonian fluids, viscosity is defined as the measure of the internal fluid friction, which is the constant of proportionality between the shear stress at any point and the velocity gradient (Tassios and Goletz Jr . (1977)). In the literature, absolute viscosity is generally symbolized by /J. arid kinematic viscosity is denoted by u and this common practice has been adopted in this chapter. Conversion from one to the other is obtained through the following relation: ' v=t (3.5) P A knowledge of the viscosity is essential for fluid flow and heat transfer calculations inherent to this project. Although many calculation procedures for bi tumen and heavy oi l viscosity have been presented in the literature, most of them are not applicable to the fluids studied here. Some of them are based on parameters such as boiling points, molecular weight, specific gravity, and accentric factors which are not available for p i tch and C H G O . Also, most of the available data used to derive or to evaluate these procedures have been measured at temperatures lower than 200° C on lighter fractions than C H G O and pitch. Therefore, given the very high sensitivity of the viscosity of heavy fractions of petroleum to temperature change, extremely large errors are bound to occur when extrapolating to temperatures in the range 300-350°C where the fouling runs were carried out. Al though measurements were obviously needed, the determination of viscosity of highly viscous materials handled at such high temperatures is difficult as explained by Miadonye and Puttagunta (1996). In Section 3.3.1, new data are presented for the effect of temperature on the viscosity of pitch, C H G O , and their blends in the temperature range of 80-340° C . Model ing of the data was attempted and the results are given and discussed in Section 3.4. 3.3.1 High Temperature Viscosity Measurements The viscosity data were obtained at atmospheric pressure using a Rotovisco RV12 from Haake Co. using the viscosity sensor system M V 400 I. This sensor system was designed Characterization of Feed Materials 25 for viscosity measurements from -60° C to 300° C and could be used wi th or without an inert gas cover. It consisted of a rotor and cup which were surrounded by an electronically controlled metal block heater, and temperature control was maintained by means of a thermistor control T P 2 4 from Haake Co. . For a Newtonian fluid in the absence of turbulence, the rate of shear D ( s _ 1 ) is directly proportional to the shear stress r (mPa) and the viscosity is defined by the Newton equation: " - % = Ri <3-6> During each test, the value of the torque S is plotted against a series of preset test rota- tional speeds n and the viscosity is obtained by mul t ip ly ing the slope by an 'instrument factor' K, specific to each drive unit and sensor system. The calibration was carried out wi th a standard l iquid of known viscosity and the factory calibration factor A'=1374 (mPa-s/scale grad.-min.) was confirmed. More details on the equipment and proper measuring procedure can be found i n the Haake Rotovisco Instruction Manual . A l l measurements generated linear n — S diagrams (see Figure 3.2), indicating Newto- nian fluids. This result is consistent wi th the literature since bi tumen is generally regarded Torque S versus rotor speed n. n, min' Figure 3.2: A Typica l n-S Diagram (T = 190°C). as a Newtonian fluid (Miadonye and Puttagunta (1996)). Table 3.2 contains the detailed viscosity-temperature data and all of the viscosities are plotted against temperature in Figure 3.3. The kinematic viscosities were obtained from Equation 3.5 by using density relationships established in Section 3.2. Characterization of Feed Materials 2b Table 3.2: Dynamic viscosity (mPa-s)-temperature data for pi tch, C H G O , and their blends. Temperature °C %wt. pitch 0 25 51.7 75 100 80.0 25.9 130.9 1187 19116 - 100.0 12.7 52.2 340.0 3429 - 110.0 - - - - 43462 120.0 - - - - 17727 128.0 6.1 - - - - 130.0 - 18.6 85.0 519.6 7581 160.0 3.3 9.1 32.2 134.6 1129 190.0 2.9 5.1 16.3 52.6 300.9 220.0 - 3.2 9.6 24.9 106.5 250.0 - 2.9 6.7 14.6 49.1 260.0 2.4 - - - - 280.0 - 2.6 4.9 9.3 27.4 290.0 2.1 - - - - 310.0 - 2.4 3.9 6.5 15.9 340.0 - - - 4.0 10.4 Viscosity of Pitch, Coker Heavy Gas Oil (CHGO), and their blends (%wt. Pitch). 1 1 — 1 — 1 1 o CHGO A 25% V 51.7% X 75% 0 Pitch — Dutt (1990) 1 1 1 1 1 O * 0 • 1 1 _l I I I I I 100 150 200 250 300 350 Temperature, °C Figure 3.3: Kinemat ic viscosity-temperature data; fitted lines obtained using Dutt 's (1990) equation and parameters given in Table 3.4. Characterization of Feed Materials 27 3.4 Modelling Viscosity Data The viscosity prediction of pitch, C H G O , and their blends based on some readily available characterization would be most convenient. Reviews of viscosity correlations and calcu- lation methods for the viscosity of petroleum liquids have been given by Mehrotra et al . (1996) and Miadonye and Puttagunta (1996). Due to the complicated and undefined na- ture of heavy petroleum liquids, their viscosity is usually calculated from semi-empirical models or empirical equations. Most semi-theoretical models for l iquid petroleums are based either on the corresponding state approach or on the modified Chapman-Enskog theory. These methods require boiling points and therefore can not be applied to heavy oils and pitch which, unlike light crude oils, cannot be distilled completely (Miadonye and Puttagunta (1996)). Also, in the corresponding state approach, the M W , S G , and N B P for each of the pseudo components characterizing the whole heavy petroleum l iquid must be available for calculating cri t ical parameters ( T c , P c , V c ) and the accentric factor. This is not the case wi th C H G O and pitch. Empi r i ca l methods make use of the many relationships that have been proposed to correlate viscosity and temperature and, in few cases, the parameters have been general- ized. However, the parameters are essentially expressed in terms of average boiling points which are not available for pi tch and blends wi th C H G O . This prevents the application of those methods or similar generalizations of parameters. The objective of this work was to develop an estimation method for the correlation and prediction of the viscosity of the fluids studied based on the experimental data obtained and other available information. 3.4.1 Evaluating Empirical Equations The first step in modeling was to find an equation that would correlate reasonably well the viscosity data over the whole measurement temperature range and for a l l the com- ponents and blends. For that purpose, several empirical equations previously used for viscosity modeling (Miadonye and Puttagunta (1996)) were tested and some of them are summarized in Table 3.3. The constants were regressed in all the equations and are listed Characterization of Feed Materials 28 in Table 3.4. Throughout the literature, the criterion for evaluating the adequacy of a viscosity calculation procedure is the average absolute deviation ( A A D ) defined as: 1 N AAD = 100 X — ^ | pexp - HCOrr I /Pexp (3.7) t'=l Table 3.3: Summary of Some of the Viscosity Correlations Tested Author(s) Equation Comments Dut t Inv — A + JT^C v is viscosity in m m 2 / s , T in °C Dutt Mix tu re lnvm - YTj=\ xi ^nvi Xj is the mass fraction of component j Herschel log p. — A + B logT T in ° F , p, in poise, A and B are constants Li tovi tz fi = A exp /i in mPa-s, T in K , A is a constant, R is the gas constant, a is activation energy Mehrotra log log(/i + 0.7) = bi + b2 logT ii in mPa-s, T in K , b i and b2 are constants Mehrotra Mix tu re log{pm + 0.7) = J2'j=i xi l°9(Pj + 0-7) Xj is the mass fraction of component j Vogel lnp = A(^ + Tlc) u in mPa-s, T in K Puttagunta logv = / , , T - 3 O v j + c V '303.15 / C=-3.002; b=log/ i 3 o°c - C s=0.0066940 b + 3.5364 p in Pa-s, T hi °C Andrade Inv = InA + (j;) v in m m 2 / s , T in °C, Andrade Gen. A=-0.4004 % w t p 2 + 0.2699 %wt p + 0.9204 13=803 % w t p 2 + 226.33 %wt p + 287.86 R 2 = 1 R 2 = 0.9937 Characterization of Feed Materials Table 3.4: Constants Regressed in the Viscosity Correlations Tested %wt. 0 25 51.7 75 100 pitch A 185.6 279.3 488.5 671.5 863.9 Vogel B 942341 942341 942341 942341 942341 C -296.8 -297.9 -286.1 -287.3 -304.4 Herschel A -2.099 -3.387 -4.924 -6.369 -8.094 B 3.962 7.559 11.976 16.3 21.516 Litovitz In A -0.255 -0.574 -0.389 -0.522 -0.390 a 1.199E+09 194E+09 2.687E+09 3.75E+09 5.11E+09 A 0.359 -0.597 -1.084 -1.840 -1.951 Dutt B 147.2 475.1 851.7 1299.8 1565.0 C -31.267 5.087 23.802 30.872 13.870 Puttagunta (Pa-s) 0.27067 4.44142 202.10 25312.95 63353826 Mehrotra bi 6.1121 8.1486 8.3472 8.9351 8.8042 b 2 -2.3667 " -3.0850 -3.0917 -3.2613 -3.1528 Andrade In A -0.0831 -0.4890 -0.3937 -0.7095 -1.3843 B 266.0 440.3 613.2 872.0 1337.0 The criterion was computed for all equations applied to each oil fraction. It is shown in Table 3.5 wi th the average deviation for each method. In the following paragraphs, each of them wi l l be discussed. • A S T M or Walther Equation Mehrotra et al. (1989) applied the double-log equation to correlate the viscosity of Cold Lake bi tumen and its fractions and the two parameters, &i and 62, were related to the molar mass. They reported overall A A D s wi thin 6%. This is consistent wi th the A A D results for pitch and 75%wt. pi tch mixture. Also , Mehrotra et al . (1989) applied a linear regression to their data for C L bitumen and the results are shown i n Figure 3.4 along with the results obtained in this work. The measurement temperature range (°C) is indicated. Over the whole measurement temperature range for our results, the parameters obtained for pitch and 75%wt. pitch blend are close to the values they reported for Cut 5. However, as the pitch content decreases, the fit becomes unacceptable as indicated in Table 3.5 and Characterization of Feed Materials Table 3.5: Average Absolute Deviation ( A A D ) for Correlations Tested %wt. pitch Equation 0 25 51.7 75 100 Average Vogel 7.7 18.6 19.1 34.9 23.6 20.8 Mehrotra 24.3 17.7 9.7 6.2 6.2 12.8 Mehrotra Mixture n/a 69.4 57.7 60.8 n/a 62.6 Dutt 8.5 10.0 3.0 4.0 1.4 5.4 Generalization 1 29.0 36.4 18.1 7.3 12.3 20.6 Generalization 2 10.4 10.7 9.3 7.2 20.6 11.7 Generalization 3 12.3 17.8 4.0 8.6 3.8 9.3 Dutt Mixture n/a 55.2 47.9 52.6 n/a 51.9 Puttagunta 19.2 13.9 8.7 14.4 22.3 15.7 Litovitz 18.5 12.6 7.6 7.9 7.6 10.8 Herschel 26.4 25.5 24.1 34.4 33.5 28.8 Andrade 12.7 10.4 8.8 16.5 4.7 10.6 Andrade Gen. 21.5 15.5 9.2 28.9 10.6 17.1 the parameters deviate significantly from the range of values they reported. Now, the max imum measurement temperature for their heaviest cut was 210°C and around 100°C for the lighter cuts. W h e n the correlation is applied to our data up to 220° C for 52 and 25%wt. pitch mixtures and up to 160°C for C H G O , the A A D s become wi th in the values they reported. Also , al l the regressed parameters become consistent wi th their results. It b versus b 2 for Cold Lake bitumen and its fractions (Mehrotra et al. (1989)), Pitch, CHGO, and blends (current work). -2.5 -3 N-3.5 -4 -4.5 CL bitumen Pitch (110-340°C) 75% (80-340°C) 52% (80-310°C) 25%(80-310°C) CHGO (80-290°C) 52% (80-220°C) 25% (80-220°C) CHGO (80-160°C) Best fit CL bitumen .Cut 5 (120-210 oC) + x Whole CL bitumen (24-121 oC) Cut 4 (30-106 oC) Cut 3 (26-100 oC)| Cut 2 (30-90 oC) Cut 1 (22-94 oC) | 9 b. 10 11 12 Figure 3.4: Parameters b{ and b2 from Mehrotra et al. (1989) and from this work. Characterization of Feed Materials 31 is suggested that the double-log equation can only be applied to heavy cuts such as pitch and the 75%wt. pi tch blend over the full temperature range involved; for lighter fractions, the correlation should not be used over the full temperature range and for extrapolation. Puttagunta et al . (1993) proposed a correlation which was shown by Mehrotra (1994) to be essentially the Walther equation. The correlation requires one viscosity data point at 30°C and was found by iteration for each oi l fraction. As shown in Table 3.4, the viscosity at this temperature is extremely high for fractions wi th high pi tch content and the A A D s show that the correlation is not well suited for the data. Furthermore, no compositional dependence or mix ing rule is provided, imply ing that one viscosity datum is required for every new mixture (Mehrotra et al. (1996)). • Andrade and Vogel Equations A l l a n and Teja (1991) calculated the viscosity of several crude o i l fractions wi th A A D s of 5-15% by using their Effective Carbon Number ( E C N ) approach to estimate the coeffi- cients in the Vogel equation. However, Gregory (1992) showed that the method gives an incorrect viscosity-temperature trend for E C N > 2 2 . Since the E C N values for the fluids studied were found greater than 22 and given the A A D s obtained (see Table 3.5), this form of the Vogel equation should not be used. The Andrade equation was applied to model the kinematic viscosity of several crude oil fractions by A m i n and Maddox (1980) and Beg et al . (1988); overall A A D s between 5.5% and 11.1% were obtained. A n average A A D of 10.6% was obtained for our data but the parameters could not be generalized. Also, Mehrotra and Svrcek (1988) showed that an Andrade-type equation was inadequate to model the effect of temperature on the viscosity of bitumens. Dutt (1990) applied the Vogel equation to model the kinematic viscosity of crude oi l fractions using the 50% boiling point as the only input. W i t h parameter C obtained as per Tassios and Goletz Jr. (1977) and parameters A and B generalized, overall A A D s between 3.8% to 6.8% were obtained. The method was applied to C H G O using the S I M D I S T curve (see Figure B . l ) , but the data could not be fitted linearly. Also, the regressed constant C for C H G O in Table 3.4 did not predict the 50% boiling point based on the Goletz-Tassios equation. Note that a S I M D I S T curve was not available for pi tch as is usually the case Characterization of Feed Materials 32 for cuts having very few constituents wi th B P < 5 5 0 ° C (Mehrotra et al . (1989)). However, by fitting to the data the equation used by Dut t , the best average A A D of 5.4% was obtained wi th a max imum of 10% as indicated in Table 3.5. The parameters could also be generalized as w i l l be shown later. The correlated viscosities are shown as smooth curves in Figure 3.3. • Other Correlations The correlations by Herschel (1922) and by Li tovi tz (1952) were not retained as suitable equations for modeling the viscosity of pitch, C H G O , and their blends. Al though the Li tovi tz equation gave an average A A D of 10.8%, the parameters could not be generalized. 3.4.2 M i x t u r e Viscos i ty Equations Several l iquid-mixture viscosity correlations are available for calculating the viscosity from the component viscosity data. Some of them require viscous interaction terms and are not applicable to bi tumen fractions (Mehrotra et al . (1989)). Most of the simple correlations for l iquid-mixture viscosity can be generalized (Reid et al . (1977)) as: n /()«".) = £ s i J > ; ) (3-8) J=l where f(/.i) may be (/i), (1/V), ln(/j,), log(n), etc., and Xj may be either of the l iquid volume, mass or mole fraction. A n equation proposed by Mehrotra et al . (1989) was applied to the calculated viscosi- ties from the double-log equation. A similar approach was used wi th the Vogel equation (Dutt (1990)). In both cases, the A A D s were extremely high as seen i n Table 3.5 and the approach was abandoned. The results achieved by Mehrotra et al . (1989) were also in that range. 3.4.3 General izat ion of Parameters A generalization of parameters was attempted wi th the Andrade and Dutt equations. The results were more successful wi th the correlation used by Dutt (1990) as shown in Table 3.5. Several generalizations were performed and they are summarized in Table 3.6. Characterization of Feed Materials 33 The best fits for parameters B and C were obtained wi th linear and quadratic functions of the weight fraction of pitch, respectively. This was the only characterization parameter available for generalization. For parameter A , the lowest average A A D of 9.3% was achieved wi th the third generalization, although the second generalization gave slightly lower A A D s for C H G O and the 25%wt. pi tch blend. The following model is therefore recommended for the viscosity prediction of C H G O , pi tch, and any blend of the two, especially for those wi th a high pitch content: B Inu = A+T + c A = -0.1885 • (InB)2 + 1.3342 • InB - 1.6161 B = 1463.08 • xp + 131,2386 C = -133.56-x ' 2 , + 179.93 • x„ - 31.56 (3.9) (3.10) (3.11) (3.12) Here xp refers to the weight fraction of pitch, T is in °C, and v is in m m 2 / s . This model covers a wide temperature range—up to 340°C—and accounts for the compositional effect. Figure 3.5 shows how well the data are fitted using these generalized parameters. Table 3.6: Generalization of Parameters i n Dut t Correlation. Generalization Equation Comments 1 A=-2.3458-zp+0.1584 B=1463.08 xp+131.2386 C=-133.5612 x-2 +179.93xp -31.56 R 2 =0.950 R 2 =0.994 R2=0.995 2 A=-0.9386 1nB+5.0524 R 2 =0.958 3 A=-0.1885-(lnB)2+1.3342 1nB-1.6101 R 2 =0.993 Characterization of Feed Materials 34 Viscosity of Pitch, Coker Heavy Gas Oil (CHGO), and their blends (%wt. Pitch). Temperature, °C Figure 3.5: Kinematic viscosity-temperature data; fitted lines obtained with Equations 3.9 to 3.12. Chapter 4 Development and Operation of the Fouling Unit 4.1 Original Apparatus Init ial experiments were performed wi th the recycle flow loop shown in Figure 4.1 which had been designed and installed by others (see Yue and Watkinson (1998)). The test fluid was kept at a constant temperature in a 2.5 L stainless steel stirred tank and heated by two ceramic elements. A gear pump for high temperature (Vik ing pump series 115, model G115, capacity of 1.8 U S G P M at 20 psi) driven by a 1/2 H P , 1750 R P M electric motor pumped l iquid through a test section consisting of a 1.10 m long vertically mounted 1/4 in . O . D . stainless steel tube (0.5334 m m I.D.). The test section was heated externally over 0.46 m of its length by a quartz sand fluidized bed surrounded by two ceramic heaters. After being heated during upflow in the test section, the test fluid returned to the tank supply. When necessary, a water cooler was used to avoid temperature build-up, and an in-line filter could be used for suspended solids removal. The first bypass configuration included a pressure relief valve and a needle valve in series to prevent eventual pressure bui ld up (e.g. in case of blockage) and to allow the excess flow to return to the tank. The first tests and experiments carried out made it clear that the original design could not properly handle the viscous fluids studied nor reach the desired temperature conditions, and it exhibited several fluctuations that made the analysis of the results difficult. Also , the design did not permit convenient verification of the flowrate and, given the nature of these experiments, safety and data monitoring were inadequate. Therefore, instead of studying the effect of process variables on fouling, most of the experimental work in this project has been devoted to improving the unit and evaluating its abil i ty to generate fouling results. Several equipment malfunctions such as two pump failures and breakage of the fluidized bed heating system required rebuilding of parts of 35 Development and Operation of the Fouling Unit Filter Water Out Vent Supply Tank b, out Gear Pump AR - Air Regulator BV - Bypass Valve FB - Quartz Sand Fluidized Bed OP - Orifice Plate P - Pressure Gauge PRV - Pressure Relief Valve R - Rotameter Rec. - Receiver Tb - Bulk Temperature TC - Thermocouple TS - Test Section * Fluid Bed Equidistant Thermocouples Figure 4.1: Original Apparatus Development and Operation of the Fouling Unit 37 the unit , and hindered the course of this project. This chapter describes the unit in detail and discusses the modifications made over the duration of the project. It ends with a diagram representing the final state of the loop which summarizes al l the changes made. 4.2 Liquid Flowrate Measurement To provide a measure of the l iquid flowrate in the test section which could verify the actual flowrate, a high temperature three-way valve (Swagelok, model# SS-63XTS8-F8) was inserted downstream of the test section. A t the end of each run or during calibration of the orifice, the flow was diverted into a 1 L pyrex beaker. Initially, only a volumetric flowrate could be measured; since the quantity of l iquid available is small , this leads to important inaccuracies in the time and volume measured. Also , the flowrate measured in this manner would have to be corrected to give the true flowrate, since the temperature in the test section was higher than the temperature in the beaker. These problems were solved when a digital balance (A & D Co. , ser.# J8003182) connected to a computer was used to record the mass collected versus time; the mass flowrate measurement was obtained from the slope of a plot of weight versus time and required a small amount of l iquid. The data acquisition was done using Lab Tech Notebook version 5.0. 4.3 Pressure Drop Measurement Initially, the pressure drop across the orifice plate was measured by two silicone filled pressure gauges. However, due to the high viscosity of the fluid studied, the gauges were often blocked preventing pressure drop measurements to be obtained for flowrate estimation and monitoring. A new scheme involving a differential pressure transducer ( D P T ) was designed and implemented successfully. 4.3.1 Differential Pressure Transducer Design, Operation, and Calibration The D P T (Omega Eng. , model# PX771-025DI) was connected to the orifice plate via two 1/4 in . tubes which were wrapped wi th heating tape to reduce the viscosity of the Development and Operation of the Fouling Unit 38 fluid during the startup period. Zero differential pressure was set from the bal l valve (Swagelok, model# SS-4P4T) connecting both lines, while the two remaining ball valves allowed air removal through the sampling valves and prevented possible damage to the D P T from excess pressure. Since the D P T was incompatible wi th the highly viscous fluids involved, the lines were filled wi th coker heavy gas oi l which is less viscous than the test fluid. Dur ing filling, traces of air were removed using the D P T purge valve. The D P T was factory calibrated and a linear relationship was used to convert the 4-20 m V output to 0-25 psid. The readings were confirmed by applying known pressure loads to the cell between 0 to 25 psid. 4.4 L i q u i d Flowrate Es t imat ion Combining the techniques described in the last two sections provided a method to estimate the flowrate that proved reliable and accurate. A relationship between mass flowrate and pressure drop was obtained. During calibration, care was taken to ensure that the temperature conditions remained constant. During the course of this study, two orifice plates were used. The first eleven ex- periments were done wi th a 1/8 in . diam. orifice plate (B—0.2); however, as no fouling seemed to form in the test section, lower fiowrates were studied, requiring a 1/16 in . diam. orifice plate (0=0.1) to be used for the remainder of the project. B o t h orifice plates were calibrated under the conditions of their use and the calibration curves are shown in F ig - ures A . 2 and A . 3 . As seen on Figure A . 2 , the larger orifice plate gave two curves for the same temperature conditions. The upper curve was discarded as measurements done at the end of some runs showed that the other was more consistent. The smaller orifice plate was calibrated under two operating temperature conditions and measurements at the end of some runs also revealed that both curves were constant. 4.5 Tes t Section and F lu id ized B e d The test section was a 1/4 in . O . D . stainless steel tube 1.10 m long (0.01 in . wall thickness T P 316/316 L Seamless, 0.5334 m m I.D.) heated by quartz sand particles (d p=349 fj.m, Development and Operation of the Fouling Unit 39 density=2631 k g / m 3 ) contained in a 0.46 m longx0.05 m I .D. stainless steel cylinder. Figure 4.2 shows the details of the fluidized bed and test section. The test section was replaced wi th a new one for each experiment. Operating temperatures were obtained from two ceramic heating elements surrounding the cylinder and by preheating the air upstream of the air distributor. A i r flowrates were measured using a calibrated rotameter (Porter Instrument Co. , model # B-250-6) which has the calibration curve shown in Figure A . l , and a pressure gauge was used to correct for the bed back pressure. A pressure regulator (Bellofram Co. , par t# 241-960-068, range 0-60 psi) was used to maintain a constant air pressure to the rotameter. 4.5.1 A i r Distributor Four 1/8 in . O . D . stainless steel tubes having two 0.6 m m diam. holes were used to introduce the fluidizing air into the bed (see Figure 4.2). The pressure drop across the distributor was estimated using the following equation K u n i i and Levenspiel (1991) based on orifice theory: where the orifice coefficient, Cor, is selected from a table as a function of the vessel Reynolds number, Rev = DvUp9/pg for the total flow approaching the distributor. The results of these calculations are shown i n Table 4.1 for different air flowrates, raai>. AP^ist represents a significant portion of the total pressure drop, or APt = APV + APcycione. According to Zuiderweg (1967), in the early years of fluidization engineering, rules of Table 4.1: Est imation of Pressure Drop Across A i r Distributor 771 air AP, Uor APd,-„ APdi,t/APt (g/s) (psid) (m/s) (psid) (%) 0.206 5.7 97.3 1.39 24.4 0.297 8.1 125.3 2.58 31.8 0.484 12.8 169.5 5.69 44.4 0.526 13.7 178.4 6.51 47.5 0.663 17.0 201.4 9.26 54.5 Development and Operation of the Fouling Unit 40 Test section (1.10 m long) 0 0.635 Swagelok sealing Outlets for test section, air, thermocouples, and thermocouple wires A, B, C - 1/16" Type K thermocouples (top, middle, bottom respectively) D, E, F - 26 gauge type K thermocouple wires (Runs 16, 20, 23 only) Dimensions are in centimeters Figure 4.2: Test section, fluidized bed, and air distributor. Development and Operation of the Fouling Unit 41 thumbs were followed, such as: APdist = (0.2 - 0.4) • APV (4.2) The current distributor clearly exceeds the design recommendation and the gas velocity at the nozzle, Uor, also exceeds the jet velocity from orifices in commercial distributors (up to 30-40 m/s) . This may result i n erosion and breakage of particles and an undesirable shift in size distribution—see Chapter 4 of K u n i i and Levenspiel (1991)—, which in turn affects the heat transfer (Molerus et al. (1995)). 4.5.2 Temperature Measurement and Control For al l experiments the temperature of the bed was measured by three 1/16 in . chromel- alumel thermocouples equally spaced (11.2 cm apart) in the axial direction—see F ig - ure 4.2. The uppermost thermocouple was 11.2 cm from the top of the bed. Also , each thermocouple was approximately 1.2 cm away from the test section, although vibrations of the thermocouples due to fluidization of the sand may have affected this distance. Moreover, for Runs 16, 20, and 23, three additional thermocouples were silver soldered on the outside wall of the test section at the same axial positions as the three others to pro- vide a measure of the wall temperature. They consisted of 26 gauge type K thermocouple wires. The temperature of the air entering the bed was also measured. The bulk inlet and outlet oi l temperatures were measured by type K thermocouples located at each end of the test section. A n entrance length of 40 cm was provided to ensure a fully developed velocity profile in the heated section. The bulk inlet temperature was controlled by keeping constant the temperature in the supply tank using an analog proportioning controller wi th a 5°C display resolution (Omega Eng. , model 49 controller). The fluidized bed temperature was controlled by the middle thermocouple wi th the same kind of device which had a 10° C display resolution. 4.5.3 Modifications As wi l l be discussed in Chapter 6, evidence was obtained that a significant amount of deposit is formed when the flow of l iquid is stopped at the end of a run, i f the fluidized Development and Operation of the Fouling Unit 42 bed is at a temperature at which batch coking is believed to occur. A successful technique used to avoid this problem has been to cool the bed wi th air before shutting down the pump. To shorten the cooling period, thereby reducing the chances of disturbing possible fouling deposits, a sand discharge was installed. It consisted of a stainless steel cylinder connected v ia a 1/2 in . tube to a 1/3 in . N P T hole dril led at the bot tom of the bed. The container was also provided wi th an air outlet consisting of a piece of tube filled with stainless steel wool. This prevented ejection of hot sand dust from the sand discharge. The choice of the valve separating the sand discharge from the bed was complicated by the high temperatures involved (500-600° C ) . The difficulty was resolved by using a gas cock valve made of brass which had no plastic seal. Final ly , since the temperature of the air entering the fluidized bed was found to fluctu- ate, an air mass flow meter (Matheson Co. , model 8160) was added for closer monitoring of the flowrate and to identify the cause(s) of the fluctuations. A voltage regulator (SL Waber, type PC2400) was used after it was found that some of the fluctuations were caused by variations in the power supplied. 4.6 Data Collection and Loop Monitoring Given the length of these experiments (24-60 hr), the addition of a data acquisition system to the original setup was clearly needed. To this end, temperature, differential pressure and mass flow meter measurements were sent to a Digi trend 235 datalogger (Doric Scientific) that converted analog signals from the measuring devices into digital signals. These signals were then transmitted to a personal computer to be displayed and saved at any specified time interval on the hard disk. A l l the measurements were also displayed on a local instrumentation panel that consisted of digital meters, selector switches, and pressure gauges. Due to the nature of these experiments and to an inadequate automatic safety system, during operation an operator was always present to monitor the apparatus. To improve the safety of the unit, an alarm device was designed, implemented, and tested. It consisted of a controller (Omega Eng. , model# CN76130-PV) which received an output from the differential pressure transducer. A n output from this controller was sent to a magnetic Development and Operation of the Fouling Unit 43 relay switch which controlled power to the entire system except the controller itself. When the pressure drop across the orifice plate exceeds the low and high alarm setpoints on the controller, the magnetic relay switch is opened and al l power to the system is shut down. This protects the unit from overheating in case of pump failure or oi l line blockage. If desired, the alarm can be bypassed. 4.7 Other Modifications and Final Apparatus 4.7.1 Initial Unsteady-State Period One primary objective of the fouling experiments was to measure in i t ia l fouling rates. Since meaningful values can only be determined when the system is essentially at themal steady-state, care must be taken to reduce the ini t ia l unsteady-state period when the temperature set points have not been reached. This is especially valid for this unit with constant surface temperature operation since the temperature of the deposit in contact with the l iquid is decreasing as fouling forms. A t several times during this project, the insulation of the loop was improved to reduce the start-up period. Also, the amount of l iquid added to the tank was increased from 2 to 2.5 L . The in i t ia l unsteady-state period was further reduced by pumping the stream in the bypass circuit only and diverting the flow in the loop once the setpoint was reached. These changes caused the in i t ia l unsteady-state period to drop from 200 minutes to reach 284° C to less than 50 minutes to achieve 300° C. 4.7.2 Liquid Flowrate Fluctuations Throughout this project, a major and persistent problem has been to explain and el imi- nate important fluctuations in the l iquid flowrate which confound the heat transfer mea- surements. First , an air chamber was installed in the bypass circuit to reduce the effect of pulsations caused by the pump on the pressure drop measurement across the orifice plate and to provide a readable measurement. Also, the original bypass design included a pressure relief valve (Swagelok, model# SS-4R3A5-A) and a needle valve (Swagelok, model# SS-6NBS8-G) in series as shown in Figure 4.1. The first pressure relief valve Development and Operation of the Fouling Unit 44 (nominal cracking pressure range 50-350 psig) resulted in pressures higher than what the pump could handle so that the excess flow from the pump could not return to the tank and damage was actually done to the pump. A more appropriate relief valve (Swagelok, model# S S - R L 3 M 4 - F 4 , cracking range 10-225 psig) was therefore installed allowing the excess flow to return to the tank and lowering the operating pressure in the bypass circuit. In order to reduce the fluctuations in the l iquid flowrate, the bypass circuit was com- pletely redesigned. The pressure relief valve and the needle valve were installed in parallel. The effect of this modification on the results wi l l be discussed in Chapter 6. 4.7.3 Viscosity Reduction O n several occasions, the pump could not be started due to the high viscosity of the test fluid involved. Heating tapes were installed around the bypass circuit and the tubing upstream and downstream of the pump. This section of the loop could be heated before starting the pump to reduce the viscosity of test l iquid trapped in this section of the loop which would otherwise prevent the pump from starting. 4.7.4 Volatilization Final ly, as higher feed temperatures were studied, a significant amount of in i t ia l feed was volatilized from the tank vent. This phenomenon led to an insufficient amount of l iquid left in the loop and certainly changed the properties of the test l iquid over the duration of the run. In order to minimize this effect, a water condenser consisting of a 3/8 in . tube in a 1.5 in . pipe (shell) was installed vertically on the supply tank. The volatiles condensed on the wall and returned to the tank by gravity. A l l the modifications and additions to the loop described in the preceding sections are summarized in the diagram shown in Figure 4.3, which represents the final state of the apparatus. Development and Operation of the Fouling Unit AR - Air Regulator C - Condenser DPT - Differential Pressure Transducer FB - Quartz Sand Fluidized Bed MFM - Mass Flow Meter OP - Orifice Plate P - Pressure Gauge PRV - Pressure Relief Valve R - Rotameter Rec. - Receiver SD - Sand Discharge ST - Surge Tank SV - Sampling Valve Tb - Bulk Temperature TC - Thermocouple TS - Test Section * - Fluid Bed Equidistant Thermocouples Figure 4.3: Final Apparatus Chapter 5 Experimental Procedures 5.1 Thermal Fouling Measurements A fouling experiment involves three major steps which are: the preparation of the test fluid, the acquisition of thermal fouling measurements, and the cleaning and preparation of the fouling unit for the next fouling test. For each fouling experiment, 2.5 L of test fluid is prepared; for obtaining the 50:50%vol. p i t c h - C H G O blend, 1339 g of pitch is broken in small pieces and 1252 g of C H G O pre- warmed on heating plates is poured on top of the pitch. The blending is perfomed in pyrex beakers placed under a fume hood on heating plates. The mixture is made homogeneous by stirring and when it is fluid, it is then poured into the feed tank of the fouling unit. The next morning, in order to lower the viscosity of the test fluid, the feed tank heaters are turned on, the feed tank stirrer is set to low speed (percent speed=20), and the feed tank temperature controller is set to the desired setpoint. The speed of the feed tank stirrer is subsequently increased to 60 when the viscosity is reduced to facilitate heating of the test fluid. Whi le the mixture is being heated, the power to the air preheater is turned on and the air flowrate to the fluidized bed is set to a suitable value which depends on the bed temperature. The power to the fluid bed heaters is also turned on and the temperature controller is set to the desired value. A t the same time, the power to the heating tape surrounding the tubing located between the feed tank and the bypass circuit is turned on in order to lower the viscosity of the test fluid trapped in this section of the loop. It is heated for one hour allowing the temperature to reach 150°C. The power to the heating tape is controlled v ia a variable autotransformer which is adjusted manually. Then, the data logging system is started and sampling of al l the measurements is made every five minutes. When the bulk temperature in the feed tank has reached the setpoint, 46 Experimental Procedures 47 the pump is started wi th both the needle valve in the bypass circuit and the needle valve upstream of the orifice plate completely opened. The power to the heating tape discussed above is turned off and the power to the heating tape surrounding the tubing to the D P cell is turned on. A temperature of about 100° C is maintained by means of the same variable autotransformer. Then, the bal l valve connecting the two D P cell lines is opened and closed to obtain a value of 0 psid across the orifice plate. When the l iquid mixture trapped i n the D P cell lines is fluid, each of the two purge valves between the orifice plate and the transducer is opened in turn to remove traces of air, and then closed. A t that point, about 200 m L of test fluid is taken from either of these purge valves which wi l l constitute the ' in i t ia l sample'. Then, the two ball valves between the purge valves and the D P cell are opened for the rest of the run in order to create a pressure drop signal. Once a reading is obtained, the needle valve upstream of the orifice plate is then adjusted to get the desired pressure drop across the orifice plate which corresponds to a known l iquid flowrate according to a calibration curve (see Figures A . 2 and A.3) . From that moment, the test fluid circulates in the unit for 24 hours on average while the process variables are maintained constant. Towards the end of the run, a digital balance covered wi th a sheet of asbestos wrapped i n aluminum foil is placed under the three-way valve of the unit. The balance is connected to the computer and the software Labtech Notebook 5.0 is used to record the weight collected every second. This requires the data logging program for the thermal measurements to be stopped first since each program uses a different operating system. Then, a 1 L pyrex beaker is placed on the balance, the flow is diverted from the three-way valve unti l about 300 m L of l iquid has been collected, and the data are saved in an A S C I I file. - - After that, the fluidized bed and the feed tank heaters are turned off. When the fluid bed temperature has dropped below 260°C, the pump is shut down. It should be mentioned that for the first seven experiments, the pump was shut down at the same time as the fluid bed and the feed tank heaters. From R u n 22 onwards, the hot sand was dumped into a sand discharge to improve the cooling process. Final ly , the power to the unit is shut off and the air flowrate to the fluid bed is closed. Approximately 200 m L of test fluid (the 'final sample') is taken from the feed tank through the needle valve located Experimental Procedures 48 below the tank and the rest is discharged into pyrex containers. The fouling data are saved in an A S C I I file. In the next stage, the test section is removed and replaced by a new one. Also, the sand left in the fluidized bed and collected in the b in below the cyclone is removed and 1000 g of sand are added to the fluidized bed. The unit is then re-insulated and is ready for the next fouling experiment. The spent sample collected in pyrex beakers is disposed in suitable containers and the pyrex beakers are washed wi th solvents under the fume hood. When a different test fluid is to be studied, the unit is washed wi th toluene and subsequently dried wi th ambient air. 5.2 Toluene Insoluble Formation and Deposition Measurements A clean glass liner is weighed and then about 1.5 g of the in i t ia l sample is placed in the glass liner. The glass liner wi th its sample is then weighed again and submerged in a sealed flask wi th 100 m L toluene without agitation for 16 hours. The resulting suspension is filtered through a 0.2 /zm Gelman Science TF-200 (Teflon) filter at room temperature using a vacuum provided by a water aspirator as described by Sanaie (1998). The glass liner and flask container are then flushed with 50 m L toluene in order to remove any possible adhering insolubles, and the resulting suspension is also filtered through the same filter. The wall of the glass funnel containing the suspension is also flushed with toluene and the residue on the filter is washed wi th toluene unt i l the filtrate becomes clear. Then the filter and its residue are removed from the filtration system into a watch glass using a forceps, and dried for 16 hours at 90°C in air at atmospheric pressure before weighing. Also, after removing the filter from the filtration system, any possible residue stuck to the glass funnel is scraped and added to the residue on the filter in the watch glass prior to drying. These precautions ensure that all the solids precipitated by the toluene are collected on the filter. The solids left on the filter are termed the toluene insolubles ( T J ) , or coke. The same procedure is applied to the final sample. Following a fouling experiment, the inside of the test section is soaked in toluene for about 16 hours and the suspension is then filtered according to the same procedure as given above. When the test section is dried, the inside of the test section is scraped wi th Experimental Procedures 49 stainless steel wool to collect any possible residue stuck to the wall of the test section. This material is added to the residue on the filter used to filter the suspension from the test section. The solids thus obtained are termed wc and represent the amount of coke present at the end of a run in the whole test section, which includes both a heated and a non-heated portions. Note that the insolubles obtained in the runs perfomed wi th the 75 wt.% FO-10 wt.% HO-15 wt.% D A O blend were measured according to the same method except that varsol was used instead of toluene. This is because the deposits obtained with such a mixture are of asphaltene-type, which are soluble in toluene, not in varsol. After draining the varsol from the test section, it was flushed with acetone. Chapter 6 Results and Discussion Throughout this project, twenty fouling experiments were performed in which the coke formation and deposition tendencies of a mixture of pi tch and coker heavy gas oi l (50:50% vol.) were investigated by changing the surface temperature of the test section, the bulk temperature of the test fluid, the fluid velocity, and the recirculation time. For each run, the fouling process was measured by thermal measurements and the final amount of deposit was evaluated by weighing the mass deposited inside the test section; the change in the toluene insolubles content of the test fluid, which represents the coke precursor concentration, was also measured. The results w i l l be presented in the first section. In several runs, interpretation of the thermal fouling measurements was confounded by the sensitivity of the measurements to fluctuations in process variables. A n analysis of the variations in the latter w i l l be given to provide an understanding of the unit behavior, and to eliminate their effects on the thermal fouling data. The effects of a series of improvements to the high temperature fouling unit are also il lustrated. The effect of the air flowrate and temperature on the heat transfer coefficient in the fluidized bed was also investigated. The data obtained wi l l be compared to different semi-empirical models taken from the associated literature in order to discuss the possible factors that may have affected the heat transfer during the experiments. Also , the heat transfer coefficient on the l iquid side was calculated in order to check the consistency in the measurements and wi l l be compared to predictions from available correlations. Final ly, to assess the abili ty of the unit to detect fouling by thermal measurement, three experiments were carried out with a known fouling fluid. The results wi l l be given and discussed. 50 Results and Discussion 51 6.1 Fouling Tendency of 50:50%vol. Pitch and C H G O Blend 6.1.1 Summary of Fouling Runs The conditions of temperature, mass flowrate (mci>), fluid velocity in the test section (vcb), recirculation time (tr) and flow regime investigated (Recb) are summarized in Table 6.1. Table 6.1: Summary of variables investigated in fouling experiments wi th a 50:50%vol. blend of pi tch and C H G O and wi th F O - H O - D A O blend 1 . Run no. Tin ATb Tb Vcb tr rhcb Recb s.s. Q 1/Uo A T i m (°C) CC) (°C) (°C) (m/s) (min) (g/s) (min) (kW) (m 2 -K/kW) (°C) 1 520 196 7.0 198 1.61 1560 33.1 559 85 0.64 4.4 311 2 514 277 7.7 280 1.09 730 21.1 1039 200 0.40 5.3 233 3 503 245 4.5 247 1.70 740 33.8 1159 265 0.36 6.3 246 4 507 286 9.5 290 0.81 1070 15.6 849 216 0.40 4.1 180 5 499 288 4.1 291 2.31 972 44.5 2395 55 0.46 4.2 208 6 503 290 3.9 292 2.36 1057 44.5 2490 75 0.45 4.4 212 7 507 277 14.7 285 0.63 887 12.2 632 100 0.48 4.3 226 8 498 291 4.4 293 1.57 646 30.2 1690 100 0.34 5.7 203 9 503 284 13.1 291 0.69 917 13.3 731 75 0.42 4.7 215 10 502 277 19.9 287 0.48 762 9.2 487 55 0.43 4.6 216 11 502 281 16.3 289 0.48 1085 9.2 522 85 0.42 4.7 214 12 501 286 19.0 295 0.43 762 8.3 469 70 0.39 4.8 207 13 600 289 18.8 298 0.83 1123 16.0 935 120 0.75 3.7 304 14 598 282 34.1 300 0.41 1148 7.9 470 200 0.63 4.4 299 15 508 199 15.4 207 0.79 2009 16.1 311 200 0.56 4.9 299 16 615 286 33.8 302 0.40 1122 7.7 465 355 0.62 4.7 313 17 601 286 31.2 302 0.40 3359 7.7 472 300 0.59 4.6 300 18 596 329 31.0 346 0.36 3353 6.6 563 300 0.51 4.5 250 19 236 87 16.6 95 0.31 1304 5.8 206 166 0.19 6.8 139 20 449 95 73.4 132 0.17 1889 3.2 266 300 0.50 5.9 317 21 444 107 25.4 120 0.68 2019 12.7 813 200 0.66 4.5 323 22 612 348 25.6 358 0.45 2059 8.3 762 200 0.50 4.4 240 23 615 363 25.3 375 0.44 1720 8.0 824 200 0.51 4.3 238 'Only Runs 19, 20, and 21 were performed with the 15% DAO-10% HO-75% FO blend. Results and Discussion 52 The fluidized bed temperature reported, T/b, refers to the temperature in the sand which is not the same as the wall temperature. This fluidized bed temperature is the average of the three axial temperature measurements described in Section 4.5.2 and is calculated after the time the system takes to achieve thermal steady-state (S.S.). The average bulk temperatures of the test fluid entering and leaving the test section, T t n and Tout, are also calculated at steady-state and Tb represents the bulk average temperature in the test section, which is the average of T{n and Tout. ATb is the average bulk temperature difference across the test section, calculated at steady-state. The average heat flow, <3, the average inverse overall heat transfer coefficient, 1/UQ, and the average log mean temperature difference, A T / m , are also calculated at steady-state. The equations used to calculate these parameters are given in Appendix D.6. Finally, the mass flowrate, the fluid velocity, and the Reynolds number in the test section are based on the calibration measurement performed at the end of each experiment. Since one of the objectives was to establish the conditions at which significant fouling is formed, the approach adopted in the experiments was to vary the process variables in the direction in which fouling formation is believed to increase. As a result, the fluid bed temperature, the bulk temperature and the recirculation time were increased, while the velocity was decreased. For the first experiments, the average fluid bed temperature was around 500°C. As no significant fouling was observed, the temperature was increased to its maximum value of 600° C for most of the remaining runs. The average bulk temperature in the test section was set initially at 198° C and was subsequently increased to around 290° C for the majority of the runs. Since no significant fouling was detected, it was further increased reaching 375°C in the last experiment. Moreover, the velocity in the test section was varied from 0.2 to 2.2 m/s and the flow regime was laminar for all runs. Since Q was determined from the temperature rise of the oil, AT},, if flowrates were too high, and ATb was too low, then Q would be subject to significant error. As shown for Run 6, at Re=2490, ATb was around 3.9°C. Higher velocities (turbulent flow) would have resulted in an even smaller ATb which might not have been accurately measured, given a resolution of one decimal place. It is also generally accepted that reducing the fluid velocity increases the fouling tendency (see Chapter 2), hence reducing velocity was Results and Discussion 53 desirable for detecting fouling. 6.1.2 Toluene Insolubles Measurements For fouling involving coking reactions, the amount of coke precursor in the test fluid and its change with recirculation time may provide clues for an understanding. For each run, the coke precursor content in the initial and final sample was measured as explained in Chapter 5. From the knowledge of the weight of the sample and that of the coke, the concentration of coke is expressed as Weight of coke recovered TI= — *100 (6.1) b ample weight Inorganic mineral matter in the fluid will contribute to the toluene insolubles as defined above. The yield of coke is then given by (TI — TI0), where TIQ is the value of TI at time zero. Upon heating of these blends, a fraction of the initial test fluid is lost due to a combination of evaporation and bond-breaking with volatilization of light fragments, this effect increasing with the severity of conditions. This weight loss, or volatile yield, is calculated as Initial total weiqht — Final total weiqht V = — ; —, — * 100 (6.2) Initial total weight For the heavy gas oils, evaporation is expected to be a major factor, given the boiling curves shown in Figure B . l . For pitch, little evaporation is expected at the temperatures investigated, and volatilization of light reaction products will dominate. Watkinson et al. (1998) carried out batch heating experiments on 50:50% vol. pitch- virgin gas oil blends in order to determine the kinetics of coke, precursor formation. Their TI and weight loss results are reproduced in Figure 6.1 to show how those important parameters are affected by temperature and reaction time. For all runs in the present work, except one, the amount of volatile matter released was not measured and, as a result, the toluene insolubles are given in terms of the weight of the final sample. To provide a more suitable basis for comparison, the toluene insoluble results of Figure 6.1 are also shown on the basis of the final sample weight. Note that from Figure 6.1c, 250 Results and Discussion 54 (a) Experimental volatile yield for the blend of 50:50%vol. pitch-virgin gas oil. 6 0 5 0 4 0 ; 3 0 2 0 1 0 0 ( 2 0 1 5 : 1 0 5 0 ( 1.4 1.2 I — • j 1 _ _ _ _ _ - O - A " 3 8 0 ° C -O- 4 0 0 ° C • A - . - . - . .^ .rr .A. -^ .r - : . \^&-' - o •-r~• ~ A- \ \ i —I 5 0 1 0 0 1 5 0 2 0 0 T i m e , m i n . , , (b) E x p e r i m e n t a l T l % in t e r m s of t w o s a m p l e w e i g h t b a s i s ( s a m e b l e n d ) . 2 5 0 - ° - Ini t ial W t . B a s i s , 4 0 0 ° C - x - F i n a l W t . B a s i s , 4 0 0 ° C -A- Ini t ial W t . B a s i s , 3 8 0 ° C - O - F i n a l W t . B a s i s , 3 8 0 ° C 1 1 1 X He - -«» n :. . : D-. - - " : _ - a - - ~ ~~ '• =ipS = _ = =,= = =c2= = = = =T = = = =S= = = = = = = = =& 5 0 1 0 0 1 5 0 2 0 0 2 5 0 T i m e , m i n , , (c) S a m e a s F i g u r e (b); y a x i s e x p a n d e d . Ini t ial W t . B a s i s , 3 8 0 ° C - O - F i n a l W t . B a s i s , 3 8 0 ° C 1 1 1 Or A - ' - —A- " i i 0 . 8 0 . 6 i 2 0 1 5 : 1 0 5 5 0 2 0 0 1 0 0 1 5 0 T i m e , m i n . , (d) E x p e r i m e n t a l T l % v s . v o l a t i l e y i e l d in t e r m s o f t w o s a m p l e w e i g h t b a s i s ( s a m e b l e n d ) . 2 5 0 I - O - Ini t ia l W t . B a s i s - x - F i n a l W t . B a s i s r —•• • / / / / / / rr i © (9 r®= = = = & = _ . - - - © " 1 0 2 0 3 0 4 0 5 0 6 0 Figure 6.1: Batch coking experiments of 50:50%vol. P i t ch and V i r g i n Gas O i l B lend— Expts . Yue (1998). Results and Discussion 55 minutes of heating at 380°C results in T/=0.90% and, wi th T70=0.77%, a coke yield of about 0.12%. When the toluene insolubles are plotted against volatile yield in Figure 6.Id, all data calculated on the same sample weight basis collapse to a single curve. Similar results were also observed for gas oils, pitch, and other mixtures of gas oils and pi tch i n the range 360-400°C. For pitch, it was noted that toluene insolubles formation only starts after a 23%wt. loss has been reached for any of the reaction times and temperatures investigated. For the 50:50%vol. p i t c h - V G O mixture, the TI appears to increase when about 30%wt. loss has been reached, as shown on Figure 6.Id. Table 6.2 contains the toluene insoluble weight percent for the in i t ia l and final test fluid samples for al l runs performed as part of this thesis. The same results are shown in Figure 6.2 as a function of recirculation time, tr. The outliers are attributed to difficulties in the filtration procedure or contamination of the unit wi th toluene. The 95% confidence Tl% versus recirculation time, t 16 14 12 10 o • x + A V 0 T " T " initial sample Outliers T„ =498-520°C; T. =196-291 °C ID in T =598-615°C; T. =282-289°C to ' i n T =596 C; T. =329°C fb in T =612 C; T. =348°C fb „ in T =615 C; T. =363°C lb m . Q . r •>* 14 16, 3 x . # * : : : : 023 V22 15 . .x.. 95% Confidence interval to 12 . • " I •A- 18, 17] 500 1000 1500 2000 t , min 2500 3000 3500 Figure 6.2: Toluene insolubles content based on actual sample weight versus recirculation time for al l runs (50:50%vol. pitch and C H G O blend). Results and Discussion 56 interval on the average ini t ia l TI content is given where the errors were assumed N(0, cr 2). The batch coking data of Figure 6.1 did not permit prediction of the volatile yields i n the current work in order to present the toluene insoluble results for the final sample on the basis of the weight of the ini t ia l sample. For that reason, the confidence interval given cannot be directly applied to the data of the final sample. However, it can be expected that the TI in final sample would be lower if they were reported in terms of the weight of the ini t ia l test fluid sample. Table 6.2: Toluene insolubles content in the ini t ia l and final test fluid for al l runs. Run no. *TI final Run no. t l i n i t i a l *77final (%wt.) (%wt.) (%wt.) (%wt.) 1 'n.m. 0.50 11 1.44 1.36 2 n.m. 1.62 12 1.35 1.21 3 n.m. 1.21 13 1.27 1.49 4 n.m. 1.46 14 1.25 1.26 5 n.m. 1.20 15 1.44 1.22 6 n.m. 1.30 16 1.27 1.30 7 n.m. 1.05 17 1.45 1.07 8 n.m. 0.84 18 1.29 1.02 9 1.36 0.98 22 1.46 9.87 10 1.29 1.08 23 1.08 16.07 fn.m.:not measured; 'calculated based on actual sample weight. The TI measurements in the present work are consistent wi th the experimental data given previously in Figure 6.Id. The recirculation times were 3 to 14 times longer than the max imum reaction time of four hours in the batch coking experiments, however the bulk temperatures were markedly lower. In R u n 22, 23%wt. of the in i t ia l test fluid weight was recovered by condensation. This amount is lower than the total volatiles actually released since part of it could not be condensed. The data therefore suggest that substantial toluene insolubles formation only starts after a crit ical volatile yield close to 30%wt. has been reached for any reaction time and temperature. As long as a lesser amount of volatiles has been released, no significant increase in the toluene insolubles wi l l occur. Final ly, in 7 cases out of 10, a small decrease in TI was observed (see Table 6.2). So far, a reasonable account for this has not been found. Results and Discussion 57 6.1.3 Mass Deposition Measurements The total amount of coke left i n the test section (heated and non-heated sections) at the end of a run, wc, was measured for each run as explained in Chapter 5. This amount comes from any coke present in the oil residue left on the wall of the tube, and any solid or semi-solid coke-like material formed as a result of fouling. For the first seven runs, the fluidized bed was not cooled down before shutting down the pump. Also, for Runs 9 and 14, the pump was stopped during the run for a few minutes because of problems wi th the pump or the fluidized bed. From R u n 8 onwards, the fluidized bed was cooled down to approximately 260° C before shutting down the pump; to further help the cooling process, a sand discharge was added from R u n 22. The results, shown in Table 6.3, are therefore separated according to the fluid bed cooling procedure used. Table 6.3: Coke collected in test section and equivalent l iquid thickness which would give rise to wc. No cooling Cooling Run no. W o Run no (mg) (mg) 1 49 516 8 2 13 2 13 42 10 6 29 3 63 274 11 5 19 4 392 414 12 18 78 5 58 255 13 10 35 6 34 138 15 18 78 7 185 928 16 14 56 9 237 1274 17 10 51 14 684 2859 • 18 3 16 22 67 36 23 262 86 Except for the last two runs, the major difference in the magnitude of the amounts of coke collected appears to be explained in terms of the fluid bed cooling procedure used. The data suggest that a significant amount of coke is formed if the fluid bed is not cooled Results and Discussion 58 down properly when the flow of oi l has stopped. From the batch coking experiments (see Watkinson et al. (1998)) and from the knowledge that there is always a certain amount of residue left in the test section once the pump is stopped, it is concluded that most of the amounts of coke shown in the left hand side of Table 6.3 come from batch coking reactions i n the residue left on the tube wall . Therefore, these results cannot be attributed to fouling and wi l l be discarded for the rest of the analysis. In order to evaluate the amount of coke formed as a result of fouling in the remaining runs i t is useful to take into account the toluene insolubles in the final sample. If we assume that wc comes exclusively from the residue left on the tube wal l , an equivalent l iquid thickness which would give rise to wc mg of coke may be calculated: X r e s = T V „ r i- * final • presKUiL where p r e s is the density of the l iquid residue which was calculated at 20° C from Equa- tion 3.2 and L is the test section length (=1.10 m). The values of wc and xres on the right side of Table 6.3 are shown in Figures 6.3a and 6.3b as a function of total recirculation time. It can be observed that no significant increasing trend in wc exists. For fixed Tb, Tfb, v, etc., it can be expected that a longer recirculation time would result i n a higher amount of coke accumulated on the surface. Runs 16 and 17 differ only by their recir- culation t ime as shown in Table 6.1 but show no significant difference in their wc values. Also, Figure 6.3a indicates that, except for the last two experiments, al l runs resulted in approximately the same low wc value. As for xres, the values shown on the right hand side of Table 6.3 are reasonable when compared to the tube diameter (Z),=0.533 cm) and do not differ significantly from run to run as shown in Figure 6.3b. If the residue layers present on the tubes at the end of the runs had such thicknesses, then the higher wc values of Runs 22 and 23 were due to the TI content in the final sample and not to a larger amount of fouling. This idea is consistent with the correlation found between wc and TIfi,mi shown in Figure 6.3c. One could argue that Figure 6.3c may also suggest that the higher concentration of coke precursor in the fluid explains the higher amount of deposit on the surface. However, this would imply for Runs 22 and 23 a different (thinner) residue layer on the tube, which is not reasonable. In addition, the small values of xres and the fact that they are scattered with tr suggest that the assumption behind xres is realistic. Results and Discussion 59 300 250 200 E . 150 100 50 0 (a) Toluene insolubles in test section at the end of runs vs. recirculation time. 1 1 1 i i • 23 12 10 : D22 8 • • • •"""16' d 15 _i 18, 17 2500 3000 500 1000 1500 2000 t , min. r (b) Equivalent liquid thickness at the end of runs which would give rise to w c vs. recirculation time 3500 100 80 12 i i •23 1 1 :15 i D ' 16 • • • 17 • 10 : D 1 3 : D22 18 8° : 11 i i i i • i £ 60 x 40 20 500 1000 1500 2000 t , min. r 2500 3000 3500 (c) Toluene insolubles in test section at the end of runs vs. toluene insolubles in final sample. I I ! j — . . | I 23p_ 2 2 Q 8, 10-13, 15-18 i I I i 250 200 £ 1 5 50 100 50 10 12 14 TL „ %wt. final Figure 6.3: Mass deposition measurement analysis; run number shown besides symbol. Results and Discussion 60 Consequently, these numbers suggest very l i t t le coke formation during recirculation. As a consequence, no substantial effect of fluid velocity, bulk fluid temperature, fluidized bed temperature and recirculation time was observed. This conclusion is consistent wi th the thermal fouling measurements which indicated no significant fouling. 6.2 Analysis of Variations in Liquid Flowrate 6.2.1 Experiments with Pressure Drop Measurement Ideally, the temperature difference across the test section, AT},, should remain constant as long as no fouling has been formed. However, for several runs, this parameter exhibited severe fluctuations and most of these variations were caused by fluctuations in mass flowrate. Evidence of this was obtained by inspecting both measurements as shown in Figure 6.4 for R u n 9 and from the relationship between A T ; , and rn which is shown in Figure 6.5 for several runs; ATt, and rn are average values of AT}, and m which are calculated, for a given run, over the same time interval. The results of Figure 6.5 are expected since for small changes in ra, with U0 l i t t le affected, mCpATb is constant and therefore AT), oc (1 /m) . Figure 6.4 reveals that the change in both measurements occurs at the same time and according to an inverse relationship which is consistent with the results of Figure 6.5. The concept of cross-correlation can be used to measure linear dependence between two trends (time series). The cross-correlation function between two t ime series {Yt} and {Zt} at lag k is given by rk = xcorr(Yt,Zt-k) = var(Yt)var(Zt-k) n — k YJXt-Y){Zt.k-Z) r n n -j 1/2 J > - Yf £ ( Z T - Zf •t=i t=i (6.4) where ??. is the number of data points and Y and Z are mean functions. Values of rk near ± 1 indicate strong (linear) dependence. If rk=Q, then Yt and Zt-k are said to be Results and Discussion (a) Bulk temperature difference a c r o s s test section v e r s u s recirculation time. 1 1 1 1 1 1 R u n 9 | 1 1 1 1 i 0 100 200 3 0 0 4 0 0 5 0 0 6 0 0 700 8 0 0 9 0 0 1000 t , min r (b) M a s s flowrate v e r s u s recirculation time; no attempt m a d e to control m a s s flowrate. - • I 1- 1 1 - - R u n 9 | 1 1 100 200 3 0 0 4 0 0 5 0 0 t , min 6 0 0 700 8 0 0 9 0 0 1000 Figure 6.4: Fluctuations in AT), caused by variations in mass flowrate in R u n 9. Figure 6.5: Relationship between AT& and ra; lines from Equations 6.6 and 6.7. Results and Discussion 62 uncorrelated. In order to apply this concept to the data, the assumption of stationarity needs to be reasonable. A time series {Zt} is said to be stationary i f the mean function and the variance are constant for a l l time. A n example of a non-stationary time series is given in Figure 6.4. A common approach used to transform a non-stationary time series into a stationary one is to use the following transformation—called differencing: AZt = Zt - Zt-i for t = 2,3,--- , n (6.5) The cross-correlation function was calculated between ATb and rh and the above trans- formation was used when necessary. The results are given in Table 6.4 wi th the 95% confidence interval and Figure 6.6 illustrates typical results for a correlated and an un- correlated t ime series. For the correlated cases, the negative value and the fact that Table 6.4: Cross-correlation between ATb and m at lag zero. Run no. ro 95% CI Run no. ro 95% CI 8 -0.01 0.19 16 -0.81 0.16 9 -0.10 0.15 17 -0.01 0.08 10 -0.45 0.17 18 -0.12 0.08 11 -0.88 0.14 19 -0.12 0.19 12 -0.91 0.17 20 0.03 0.19 13 -0.26 0.14 21 -0.61 0.19 14 -0.93 0.14 22b -0.82 0.11 15 0.01.. 0.10 23 -0.56 0.14 it is only significant at lag 0 is clearly consistent wi th Figure 6.5 which shows an inverse relationship and emphasizes the above observation that the change in both measurements occurs at the same time. The large negative cross-correlation values obtained in some runs, such as 11, 12, and 14, are attributed to larger and/or more variations in l iquid flowrate. It was observed that when attempts were made to control the flowrate, varia- tions in l iquid flowrate were more important and more frequent than when no attempts were made. Attempts to control the flowrate were done in Runs 11, 12, 14, 16, and 22b. On the other hand, when the variation in flowrate was too small , no correlation was found. In order to see whether the changes in ATb wi th respect to m observed in each run are consistent wi th the results of Figure 6.5, the run average values of ATJ, and m were Results and Discussion 63 (a) Cross-correlation between mass flow and ATfc 1 0.5 -0.5 -1 ; UNCORRELATED; 95° lo Confidence limit Run 8 : -10 -5 0 5 Time lag, 5 min. 10 (b) Cross-correlation between mass flow and ATfc. 1i 0.5 -0.5 -1 CORRELATE : \ DAT LAG 35% Confic ZERO Jence limit : V 7 Run 16 \ -10 -5 0 5 Time lag, 5 min. 10 Figure 6.6: Cross-correlation function between AT& and ra for Runs 8 and 16. fitted to the following equations which are shown as lines in the same figure for the two fluidized bed temperatures: -1.02 AT(, ]5oo°c 173.1 • ra 156.0-ra - 0 . 7 7 (6.6) (6.7) The power-law equation was chosen since ra-ATft is expected to be approximately constant. The temperature difference, AT},, and ra were plotted against each other as shown in Figure 6.7 and the slope was compared to the first derivative—with respect to ra—of Equation 6.6 or 6.7. The results are shown in Figure 6.8. For both bed temperatures, the results are quite consistent given the errors in the fitted curves and in the individual runs. It must be taken into account that it was not the purpose of these experiments to Bulk temperature difference across test section versus mass flowrate. 22 1 1 1 1 r i • Run 10 Linear fit; slope=-1.9454 - :«i7^tM^v • ' . • —*—j . i i i i 7.5 8 8.5 9 9.5 10 10.5 Mass fowrate, g/s Figure 6.7: Linear correlation found between AT), and ra. Results and Discussion 64 First derivative of averaged AT f a with respect to averaged mass flow vs. averaged mass flow. i i o : 8 : O TFB=500°C : A T(B=600°C T\U=500°C ._. T)B=600C J I °5 10 15 20 25 30 35 Averaged mass flow, g/s Figure 6.8: Slopes of Equations 6.6 and 6.7 (lines) versus corresponding slope in individual runs (symbols). obtain such relationships and therefore the data was not taken under perfectly controlled conditions. Based on these results, it appears that the variation in ATb observed in these runs may have been caused by flowrate variations. 6.2.2 Initial Experiments In the early experiments (Runs 1-7), the flowrate was determined only by bourdon pres- sure gauges which measured A P across the orifice plate. Subsequently the D P cell was used. Because of frequent blockage in the gauges and other problems, the flowrate was uncertain in Runs 1-7. The available pressure drop measurements in R u n 1 revealed that the observed drop in ATb had been caused by an increase in flowrate, as shown in Figure 6.9. Hence it was concluded that in spite of the apparent increase in the foul- ing resistance, Rfc, no fouling had occurred. However, for Runs 4-7, no pressure drop measurements could be made due to blockage of the pressure gauges. In order to recover useful data from these runs, attempts were made to correlate ATj , wi th other parameters which could be related to the flowrate, rh. A measurement which was affected by the flowrate was the temperature difference between the temperature of the test fluid in the tank and the bulk inlet temperature caused by heat losses, ATioss. Hence an attempt was made to relate A T / o s s to the mass Results and Discussion 65 10 8 6 4 2 (a) Temperature difference across the test section versus recirculation time, t. - T 1 - r 1 1 ~r I - O | O Run 1 0 200 400 600 800 1000 1200 1400 1600 (b) Thermal fouling resistance calculated with a constant flowrate value (RfJ versus t.. 1 1 1 1— 1 1 i ; : : .: a . . . . : - 9*- | O Run 1 | i 1 1 1 5 o 2 DC 200 400 600 800 1000 1200 (c) Pressure drop across orifice plate versus t. ~> O 1400 1600 1600 Figure 6.9: Drop in ATJ, in R u n 1 caused by a flowrate increase. flow and to A T b in order to determine whether fouling or mass flow variations were the cause of the observed changes in ATb. A T / 0 5 S is the average value of A T / o s s which is calculated, for a given run, over the same time interval as rh. A correlation was found between A T / 0 5 S and m , as shown in Figure 6.10a for a bulk inlet temperature of about 290°C. Figures 6.5 and 6.10a were then combined to provide a correlation between A T b and ATioss caused by the same underlying variation in flowrate; the result is shown in Results and Discussion 66 Figure 6.10: Correlations found between A 7 } o s s , AT),, and m for Runs 4-11. Figure 6.10b. Hence, the following equations were fitted to the data of Figure 6.10: ATioss = 142.21 - m - 0 ' 8 4 (6.8) A T 6 = 0.91 • ATloss - 2.07 (6.9) ATiossj = 3 0 . 9 - m " 0 4 9 (6.10) Equations 6.8 and 6.9 are valid for some of the runs performed wi th the unit having its original insulation. The insulation of the unit was improved after R u n 11. Equation 6.10 applies for some of the runs done after R u n 11. ATioss was plotted versus the mass flowrate and AT), for each individual run as shown in Figure 6.11. The slopes obtained were compared to the first derivative of the above equations and the results are given in Figure 6.12. The slopes measured in the individual runs appear consistent wi th the Results and Discussion 67 (a) AT, versus mass flowrate. o 26 25 24 J23 5 22 21 20 . Hun 10 Slope=-1.79°Cs/g .. 8 8.5 9 9.5 Mass fowrate, g/s 10 (b) Bulk temperature difference across test section versus AT | o s s . 23 r 22 21 o _i20 19 18 17 • Run 10 Slope=0 95 : ? . I,. ..•*h<^ !«•» * « Jr 1:. 21 22 23 24 25 26 AT. , °C loss Figure 6.11: Correlations observed between A T / 0 S S and tin and between ATb and A T ; o s s (a) First derivative of averaged A T | O S S with respect to averaged mass flow vs. averaged mass flow. 0.5 0 O -0.5 of > -1 > "D -1.5 £2 -2 -2.5 1 Derivative of Eq. 6.8 O Individual runs; Tb=290°C, T (b=500°C 0 8 5 10 15 20 25 30 Averaged mass flow, g/s (b) First derivative of averaged A T B with respect to averaged A T | Q S S VS. averaged A T | O S S . 1.5 0.5 -0.5 O .4. -©- 9 : 7 •:0 1 s t Derivative of Eq. 6.9 O Individual runs; Tb=290°C, T (b=500°C 10 O . .14 16 17 18 19 20 Averaged A T 21 22 23 loss' 35 24 Figure 6.12: Slopes of Equations 6.8 and 6.9 vs. corresponding slopes in individual runs. Results and Discussion 68 corresponding relationship. This suggests that the drop i n AT0 observed i n runs such as 4 and 7 were caused by an increase in flowrate. Figure 6.13 shows both temperature differences versus time for Runs 4, 7 and 10. The preceding discussion revealed that in R u n 10, the variation i n A T I was caused by a flowrate variation and Figures 6.13e and 6.13f indicate that this variation produced a similar effect on ATioss. The fact that the change in both measurements for Runs 4 and 7 occurs at the same time and given the above comparison of slopes suggest that the variation i n AT0 in those experiments was also caused by a variation in flowrate. 6.2.3 A R M A Model and Variable Flowrate Approach In order to distinguish fouling from flowrate variations effects, a procedure was developed in which two different techniques were applied to the data. Once pressure droj) measurements were available, the natural way to distinguish foul- ing from flowrate effects, which was applied to the data as a regular part of the work, was to calculate the heat flow (Equation 2.1) based on the actual flowrate. The effect of this approach is shown i n Figure 6.14. This approach works as long as the change i n flowrate is such that rh • CpATb is approximately constant. When the variation in flowrate is too large, a significant change in the heat flow occurs; an example of this is shown in F ig - ure 6.15 which is a plot of the average heat flow, Q, versus the average mass flowrate, rh. The increase in heat flow wi th mass flowrate shown for different fluid bed temperatures and two test fluids, is consistent wi th the fact that the heat transfer coefficient (oil side) also increases with the mass flowrate. This phenomenon is believed to be responsible for the poor results of using a variable flowrate obtained in R u n 10. Figure 6.16 suggests that the drop in flowrate (Figure 6.13f) was large enough to cause a significant drop in heat flow. Another technique used to distinguish fouling from flowrate variations consisted of modeling the temperature difference across the test section as a function of the pressure drop across the orifice plate, A P , and then using the model to compare the predicted AT& with the true AT},. Assuming that the variations in ATJ, were only caused by the flowrate, a significant deviation between the prediction and the data would indicate fouling. Since Results and Discussion b y the model represents the process under clean conditions, the modeling step was done with the initial data where fouling had not yet occurred. A block diagram illustrating Figure 6.13: Similarity of patterns in ATb, AT[oss and rh for Runs 4, 7, and 10. Results and Discussion 70 (a) Heat flow (constant flowrate) vs. time. (b) Heat flow (actual flowrate) vs. time. 0.38 200 400 600 800 1000 t, min 200 400 600 800 1000 t , min Figure 6.14: Use of variable flowrate approach to reduce the effects of flowrate on Q; for Qc, the flowrate value measured at the end of the run was is always assumed. 0.8 0.6 d 0 ) 0.4 O) a) > < 0.2 Averaged heat flow vs. averaged mass flow for different fluid bed temperatures, - i 1 1 1 1 1 ~ 14 2 0 " V " A- 12 10 o _ _ e ""•• - A - T. ~126°C; T ( 1=450°C; DAO blend b fb 0 - O - T b=290°C; T ( b=500 C, pitch/CHGO blend _rj_ T b=286°C; T(b<=600°C, pitch/CHGO blend 1:1 •21 •• •• - -O fl 13 6 8 10 Averaged mass flow, g/s 12 14 16 Figure 6.15: Relationship between the heat flow to the test section and the mass flowrate. Results and Discussion 71 AT(t) AP(t) Process (true data) v Model Without Fouling AT(t) Fouling Indication (prediction) Figure 6.17: Block diagram of principle used to distinguish fouling from flowrate effects. this principle is shown in Figure 6.17. The process was modeled according to an output error model structure ( A R M A ) which belongs to the category of black-box models (see e.g. Box and Jenkins (1970) for more background): ATb(t) = f ^ A P ^ + e(t) F(q) = i + /i<r1 + --- + /n/<rn' B(q) = b.q-1 + b2q~2 + • • • + bnbq-n" (6.11) This model is a representation of linear time-invariant systems and was chosen for simplic- i ty of identification and in the absence of a well-founded physically parametrized model. The purpose of this model was to predict changes in ATb that occur over a relatively long period of time which are signals of low frequency. Therefore, nb and rij were taken as one. The parameters are given in Table 6.5 and the application of the model is displayed in Figure 6.18 for three runs. The parameters were determined using a function called 'b j ' in M a t l a b © . The modeling data were taken up to 300 minutes where it was assumed that no fouling had occurred. The negative value of 6i indicates an inverse relationship between the flowrate and ATb which is consistent with Equations 6.6 and 6.7. F ig - ures 6.18a and 6.18c clearly show that the variation in ATb in Runs 9 and 13 can be predicted from the pressure drop data only; as a result, it can be said that no significant fouling occurred in these experiments. This procedure gave excellent results for these runs, but for some others such as 10, 11, and 12, the predictions were less satisfying (see Results and Discussion Table 6.5: Parameters regressed in Equation 6.11 for some experiments. Run no. Modeling Data Parameters Standard (min) Error 9 45 - 301 bi = -5.3926 1.8 fi = -0.6307 0.15 10 35 - 301 6i =-22.1685 3.01 fi = -0.0202 0.13 11 40 - 301 6i =-11.2571 1.23 fi = 0.1601 0.11 12 100 - 300 6i = -1.2107 0.09 fi = -0.041 0.07 13 75 - 301 bi = -0.1161 0.04 fi = -0.9132 0.05 Figure 6.18e). The poor quality of ini t ia l data can give rise to incorrect predictions of ATJ, although no fouling is formed. If ini t ia l ly the data are not rich enough to cause significant changes in ATb, the resulting model wi l l be inacurate and uncertain. This is often the case in fouling experiments since stability of variables is crucial. The greater uncertainty in parameter fi in Table 6.5 for Runs 10 to 12 than for the other runs seems to explain the poor predictions obtained. Another factor that can cause poor predictions may be non-linearities between ATI, and A P especially when large flowrate variations occur. The largest deviation between the predicted and measured ATb in R u n 10 (see Figure 6.18e) at 400 minutes is attributed to this. The relationship between ATb a n d A P observed in the modeling data does not represent the data properly outside the range of modeling data. Results and Discussion (a) Measured and predicted A"i"b vs. time (Run 9). (b)Pressure drop across orifice plate vs. time (Run 9). O 16 15 14 o13 12 11 10 . Measured Predicted Pred.± standard error 0 200 400 600 800 1000 (c) Measured and predicted AT b (Run 13). 22 21 20 O 19 < 18 17 16 15 Measured Predicted Pred.+ standard error 0 200 400 600 800 1000 1200 (e) Measured and predicted ATfc (Run 10). 23 22 21 O 20 < 19 18 17 16 . Measured Predicted Pred.± standard error 0 200 400 600 800 200 400 600 800 1000 (d) Pressure drop across orifice plate vs. time (Run 13). 15 r 0 200 400 600 800 1000 1200 (f) Pressure drop across orifice plate vs. time (Run 10). 0.8 r 0.7 0.6 . 0.5 1:0.4 j0.3 0.2 0.1 0 200 400 600 800 t , min Figure 6.18: Appl icat ion of A R M A model to predict ATb based on A P . Results and Discussion 74 6.2.4 Elimination of Fluctuations Finding the source of the fluctuations in flowrate discussed in this section has not been straightforward. Several hypotheses were made as to what was causing them and several changes to the fouling unit were implemented to verify those hypotheses. For example, after observing a significant hysteresis problem, the orifice plate and the needle valve used to control the flowrate were replaced after R u n 11. The first bypass design consisted of a needle valve in series wi th a spring loaded pres- sure relief valve. Dur ing operation of the unit, a fraction of the total flowrate delivered from the pump circulated in the bypass line through the pressure relief valve. The fluc- tuations in the flowrate were clearly related to the stability of the split fraction of the flowrate between the test section and the bypass. This split fraction depends on the re- sistance to flow in both sections. After several runs wi th this bypass configuration, it was postulated that the flowrate fluctuations may be caused by oscillations in the spring of the pressure relief valve causing changes in the resistance to flow in the bypass section. Concerns about the design of the bypass circuit were also raised since l iquid was not supposed to flow i n the pressure relief valve except under pressure surges (e.g. in case of a test section blockage). In R u n 17, in order to test this hypothesis, the needle valve and the pressure relief valve were therefore assembled i n parallel as described in Chapter 4 so that no flow would circulate in the relief valve under normal conditions and the excess flow would only return to the tank v ia the needle valve. In order to evaluate the change in the stability of the flowrate after modifying the design of the bypass circuit, the standard deviation of the flowrate measurement was calculated for al l experiments and the results are shown in Figure 6.19. It can be seen from these results that for the first bypass design, the flowrate was more unstable in experiments wi th lower flowrates. Also, except for the last two runs, it is clear that the new bypass configuration greatly decreased the flowrate variations and, as a result, the quality of the data was significantly improved. The improvement obtained supports the hypothesis formulated. For the last two runs, it is believed that the poorer stability of the flowrate was again caused by the pressure relief valve. The seals in the pressure relief valve were made of vi ton which is rated for 204°C max imum and this was the highest Results and Discussion 75 Standard deviation of mass flowrate vs. averaged mass flowrate for two bypass configurations. 0 -0.2 ... i ! ! ! r •A- Initial bypass • Modified bypass *11 D p 2 3 D D * i o ; i * s 20 1918 17 i 21 i i L 1 J I I 1 1 L _ 5 10 15 20 25 30 Averaged mass flow, g/s Figure 6.19: Standard deviation of flowrate versus flowrate for two bypass configurations. rating available from the manufacturer. Now, the last two runs were done under the highest bulk temperatures ever studied (358 and 375°C). It is therefore possible, i n those two runs, that the seals had reached a degradation state which allowed l iquid to flow through the valve, therefore causing the flowrate variations observed in these runs. 6.2.5 Viscosity Effect It has been shown in Section 6.2.1 that a relationship exists between the temperature difference between the tank and the test section inlet temperature, A T j o s s , and rh as shown in Figure 6.10a. Now, Runs 17 and 18 did not exhibit any correlation between ATi0SS and rh (see Figure 6.20). Al though the data for these two runs indicate an increase 12 11.5 o S 11 10.5 10 (a) A T, versus mass flowrate. • Run 17 7.5 7.55 7.6 7.65 7.7 7.75 Mass flow, g/s O 17 16 15 »14 i- < (b) A T. versus mass flowrate. Run 18 \_r/.'v. *TPi i iK 'I i T T * • - i . 6.2 6.4 6.6 Mass flow, g/s 6.8 Figure 6.20: Test for correlation between A T / o s s and m for Runs 17 and 18. Results and Discussion 76 in A T } o s s , which suggests a decrease in flowrate, the flowrate measurement appeared to be relatively constant, as shown in Figure 6.21. (a) A T, versus time. v ' loss (b) A T, versus time. v ' loss 11.5 O " 11 n 1 1 10.5 500 1000 1500 2000 2500 3000 3500 (c) Heat flow versus time. 500 1000 1500 2000 2500 3000 3500 (e) Mass flowrate versus time. 7.8 o '.7.6 7.4 7.2 Run 17 500 1000 1500 2000 2500 3000 3500 t, min 0.58 500 1000 1500 2000 2500 3000 3500 (d) Heat flow versus time. 500 1000 1500 2000 2500 3000 3500 (f) Mass flowrate versus time. 6.8 5 _o 8 6-4 6.2 i 1 1 | Run 18 | ' Si 1 500 1000 1500 2000 2500 3000 3500 t, min Figure 6.21: A T / o s s , heat flow and mass flow measurements for Runs 17 and 18. Results and Discussion 77 Now, the viscosity measurement for the in i t ia l and final samples obtained at 80.4°C for several experiments indicates that these two runs experienced the greatest drop in viscosity as shown in Figure 6.22. This viscosity reduction may be due to chemical Dynamic viscosity (80.4°C) of the 50:50%vol. pitch/CHGO blend vs. recirculation time (unsteady-state period substracted). 1 6 Q 0 — X , , 1400 1200 £ 1000 =£ 800JF 600 400 14 9 10.... 10,12 J? 22..!.... 1 2 na16 • 9 500 • 13 D 1 1 * : 14 1000 • 15 1500 t, min 2000 • Initial * Contaminated • Final 2500 : • . ; .17 .;ia.J 3000 Figure 6.22: Viscosity drop during recirculation of test fluid. changes in the l iquid, called visbreaking (see Gray (1994)). The mass flowrates were calculated from the orifice plate equation: „ TTD* / 2 p A P \ 1 / 2 where C is the discharge coefficient, Dth is the diameter of the orifice throat (= 1.588 x l O - 3 m), p is the density of the test fluid, A P is the pressure drop, and 3 is a diameter ratio (= 0.1). The discharge coefficient was measured and the results are shown in Figure 6.23. The data suggest a slightly decreasing trend with Reynolds number and this is consistent with the data reported in Perry and Green (1984) for this range of Reynolds number. During an experiment, al l parameters in Equation 6.12 are expected to be constant such that the mass flowrate wi l l be constant too. However, if the viscosity drops during recirculation of the fluid, Figure 6.23 predicts that the discharge coefficient would decrease, thereby causing a drop in the flowrate i f the A P was held constant. This effect is in agreement wi th the observed increases in A T ) o s s in experiments 17 and 18 (Figure 6.21) which suggest a decrease in flowrate. Since C is a non-linear function of Pe t / , , as shown in Perry and Green (1984), the data of Figure 6.23 were fitted to the following equation shown as a line in the same figure Results and Discussion 78 Orifice plate discharge coefficient (D =1/16", p=0.1) versus Reynolds number for the 50:50%vol. pitch/CHGO blend. 0.8 0.7 O 0.6 0.5 0.4 .Q.. 10 o Q18 10 Re., Figure 6.23: Discharge coefficient vs. Reynolds number for the 1/16" diam. orifice plate, only over the narrow range of Reynolds number that included these two experiments: C Reth -0.287 • log(Reth) + 1-542 4m TrpDthv Equation 6.12 can now be rearranged as: 4m (6.13) m = -0.287 • log- 1.542 7T D th TTpDthU The relative change in m during a run can be expressed as: -0.287 • log (^) [2pAP\1/2 (6.14) rrif — mo rtif (6.15) -0.287 • log ( + 1-542 where the subscripts 0 and / refer to ini t ia l and final respectively, and where p is given by Equation 3.2 and uQ by Equation 3.9 in which A , B , and C are given in Table 3.4 for the 50:50%vol. blend (Dutt equation). The corrected in i t ia l viscosity at T , n , fo.co was calculated by correcting the calculated ini t ia l viscosity at T,-„, fn,c> by a percentage obtained from the calculated and measured in i t ia l viscosities at 80.4°C, Changecm. The corrected final viscosity at T , n , VfiCC, was calculated by correcting the corrected ini t ia l vis- cosity at Tin, i^o,cc, by a percentage obtained from the measured in i t ia l and final viscosities at 80.4°C, Changeof. The results are given in Table 6.6. Results and Discussion Table 6.6: Measured and calculated in i t ia l and final viscosities for Runs 17 and 18. 80.4°C Run no. T i n VO, c Changecm Changeof vo ,cc Vf.cc (°C) (mm 2/s) (mm2/s) (%) (mm2/s) (%) (mm 2/s ) (mm2/s) 17 286 1196 1199 0.3 911 23.8 5.27 4.02 18 329 1611 1199 -34.4 345 78.6 5.08 1.09 'm: measured; c: calculated; cm: calculated to measured; 0: initial; / : final; 0/: initial to final; cc: corrected. The value of the ini t ia l flowrate, m 0 , was searched by trial and error and a satisfactory value was obtained by minimizing the absolute value of the difference between the left and the right hand sides of Equation 6.15. The value of the final flowrate was measured at the end of each run. Table 6.7 gives the results of these calculations as well as the predicted change in rn based on the change in ATioss, which is based on Equation 6.10: Am*T'°°° = {-^oJ-)0 -{-^oJ-)f ( 6 - 1 6 ) Table 6.7: Predicted decreases in flowrate in Runs 17 and 18 based on two approaches. Run no. LHS RHS |LHS-RHS| m / rh0 Ami, AmAT,,,,, (g/s) (g/s) (g/s) (g/s) 17 -0.044 -0.044 4.46xlO - 1 0 7.69 8.03 0.34 0.23 18 -0.251 -0.251 8.66xl0~ 1 0 6.47 8.09 1.62 0.43 It can be observed that both methods predict a decrease in flowrate. The deviation between these predictions may be partly due to uncertainties in Equat ion 6.10 which arise from an insufficient number of data used to derive it. For R u n 18, the greater deviation may be attributed to the fact that the data in R u n 18 are more noisy as seen on Figure 6.21. Also, Equation 6.10 represents data obtained for a bulk temperature of around 286°C which is different from the bulk temperature in R u n 18 (329°C). Moreover, the slope of the fitted line in Figure 6.23 may be higher than the actual slope since, under the Reynolds number of R u n 18, the slope appears to be decreasing. This is consistent with the results reported in Perry and Green (1984) which also exhibit a decreasing slope. A smaller slope would have resulted in a smaller value of A???.„ for R u n 18. Results and Discussion 80 Based on these results, i t is possible that the drops in viscosity in these two experiments have caused a slight decrease in flowrate and, as a result, the temperature difference across the test section increased. Since the flowrate is based on a pressure drop across an orifice plate, which was maintained constant, an apparent increase i n the heat flow was observed for these runs. Consequently, it appears that monitoring and controlling the viscosity during recirculation of these heavy hydrocarbon streams may be crucial for the correct interpretation of the fouling data. 6.3 Heat Transfer in a Bubbling Fluidized Bed As discussed in Chapter 2, in order to estimate the relative importance of the different resistances between the fluidized bed and the flow of l iquid inside the test section, three tests were performed i n which wall temperature measurements were made, as described in Chapter 4. In Runs 16 and 20, measurements were obtained for a series of gas flowrates, but for R u n 23, only one gas flowrate was used. In this section, the experimental values of fluidized bed heat transfer coefficients obtained in these tests w i l l be compared to the predictions of calculation methods introduced in Chapter 2. Also , the characterization of the test fluids of Chapter 3 allowed the use of different correlations available to estimate the clean heat transfer coefficient inside the test section. 6.3.1 Heat Transfer Coefficient Around an Immersed Tube The measured heat transfer coefficients for the three tests are compared wi th the predic- tions of some of the correlations given in Chapter 2 in Figures 6.24 and 6.25. For Runs 16 and 23, only the correlation by Molerus et al. (1995) was tested. It is well known that in the intermediate range of 10 2 < Ar < 10 5 , h0 goes through a max imum at some inter- mediate gas velocity, which is consistent with our results (see e.g. K u n i i and Levenspiel (1991) and Molerus et al . (1995)). The decreasing hQ at higher superficial gas velocities was attributed by K u n i i and Levenspiel (1991) to more contact t ime wi th bubbles with their low h values. The percentage deviation of the experimental h0 from the predicted values is given Results and Discussion 81 in Table 6.8 for the three experiments. The correlation by Vreedenburg (1960) deviates Predicted (line) and experimental (symbol) heat transfer coefficient between surface and bed vs. excess gas velocity. 0.35 600 500 400 ^.300 o ^ 200 100 Molerus etal. (1995) Molerus etal. (1995) 0.15 0.2 0.25 0.3 Calculated based on average bed and tube wall temperature. 0.35 : Calculated based on average tube wall temperature. O : : O 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 U - U „ m/s mf Figure 6.24: Measured and predicted h0 according to different methods for R u n 20. Experimental and predicted (Molerus et al.(1995)) heat transfer coefficient versus excess gas velocity. 1200 1000 ^ 800 | 600 • c ° 400 200 0 — o o _Bas.ed .on average, be d and.tube *-^cf~v wall tern pe rature. • O #16, h ; Based on T. ,„„ and T.. o.exp fb, top fb. bot V #23, h ; Based on T.. , and T„ , , o.exp fb, top fb, bot • #16, h ; Based on T,. m i . and T.. o.exp fb, mid fb, bot Run 16; Predicted * Run 23; Predicted —" 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 U - U (, m/s mf Figure 6.25: Measured and predicted h0 according to Equation 2.19 for Runs 16 and 23. Results and Discussion Table 6.8: Experimental and predicted h0 from various methods. Measured Molerus et al. (1995) Kunii and Levenspiel (1991) Vreedenburg (1960) Run h 0 h 0 'Dev. ho Dev. h 0 Dev. no. (m/s) ( W / m 2 K ) (W/m 2 -K) (%) (W/m 2 -K) (%) ( W / m 2 K ) (%) 20 0.0722 155 339 54 309 50 92 67 0.1274 233 435 46 280 17 179 30 0.2260 273 514 47 236 16 406 33 0.2453 278 519 46 227 22 459 39 0.3231 236 530 55 203 16 706 67 16 0.0248 309 266 16 0.0644 354 387 8 0.1152 438 489 10 0.1299 449 510 12 0.2282 430 589 27 23 0.2931 776 606 28 t T J m / : minimum fluidization velocity (see Appendix D.3); U - U m / is excess gas velocity. 'Dev. is deviation. significantly from the data and does not predict a max imum as found in their experimental data. Saxena (1989) attributed this deficiency of the correlation to an absence of a particle concentration term (1 — e). The correlations of Vreedenburg (1960) underestimated the data of Verma and Saxena (1983), the experimental values being about three times the calculated values. This is not the case for the data of R u n 20. Note that the correlation by Wender and Cooper (1958), which was found by Verma and Saxena (1983) to reproduce their data best, could not be tested here because of a lack of information for the bed voidage, e. The deviations of experimental data from the model proposed by K u n i i and Levenspiel (1991) were smaller, although a max imum could not be predicted. This may be attributed to the lack of data for the bubble frequency at various gas flowrates, nw. The correlation by Molerus et al. (1995) reproduced best the qualitative trend of the experimental data, although the values were significantly lower for R u n 20. The agreement for R u n 23 is much better. For R u n 16, the experimental coefficient, h „ , was obtained using two different sets of wall temperatures. Usually, the log mean tempera- ture difference, L M T D , involved in the calculation of h0 was based on the bulk inlet and outlet temperatures and on the wall and the sand temperatures at the top and bottom Results and Discussion 83 axial positions described in Chapter 4. This was the case for Runs 20, 23, and 16 (circle symbol). However, the temperature difference between the sand and the tube wall of the top axial position in R u n 16 appeared to be too small compared to the other temper- ature drops observed. This is shown in Table 6.9. For that reason, the heat transfer Table 6.9: Bed-to-wall temperature difference at three axial positions (Runs 16, 20, 23). Axial position #16 #20 #23 top 15 175 70 middle 180 210 40 bottom 100 220 84 coefficient in R u n 16 was recalculated using the middle and bottom bed temperatures measurements. The results, shown as squares on Figure 6.25, are more consistent wi th the predicted coefficient, h0. The deviations now range from -6% to +27% which is quite resonable given the accuracy of the available correlations. This suggests that the wall temperature measurement at the top of the bed in R u n 16 was not correct. The hQ values for R u n 16 marked with a circle are clearly too high. From these results, it is suspected that the wall temperature measurement may not necessarily give the actual wall temper- ature. Three new thermocouple wires were silver-soldered for each test, resulting in three welding "lumps" on the test section. It is l ikely that the variabil i ty in the position of the thermocouple tip in this spot wi l l cause some error in the measurement. In some cases, the thermocouple tip was just on the top of the lump while sometimes it was deeper in the test section. Also, in each test, the spot was covered wi th sintered quartz sand. This may have increased the thermal resistance between the fluidized bed and the wall . The significantly higher temperature gradients measured in R u n 20 may have been caused by this phenomenon, therefore causing the measured h0 to be lower than the pre- diction. Usually, h0 is calculated under the conditions of an average fluid bed temperature between the wall and the bed temperatures. For R u n 20, h0 was also calculated assuming the bed to be under the conditions of the average wall temperature only. The results are shown as a dashed line in Figure 6.24. This clearly does not account for the discrepancy Results and Discussion 84 between the experimental and the predicted values. The accuracy of the correlations by Molerus and Ma t tmann (1992) and Molerus et al . (1995) was also tested wi th a set of independent data obtained by Makhor in and Kharchenko (1964) wi th a spherical probe immersed in 80-cm deep and 22-cm diameter air fluidized bed of quartz sand (dp = 0.34 mm). The results are shown i n Figure 6.26 and illustrate the accuracy of both correlations. Note that the diameter of particles was between 0.25 and 0.50 m m , which is considered a narrow size distribution. Based on these results, it seems reasonable to expect our data 800 r Prediction of maximum heat transfer coefficient vs. bed temperature (O. Molerus et al. 1995). 1 1 1 r- 1 i i i ^ 7001 £ 5 600 \ 500 O Data Prediction ^ — c d 400 1 100 200 300 800 900 400 500 600 700 Bed Temperature, C Prediction of heat transfer coefficient vs. superficial gas velocity (O. Molerus et al. 1995). 1000 700 r O Data; Bed Temp^SOtfC Prediction 600 h- 500 400 300 1 0.5 U [m/s] 1.5 Figure 6.26: F i t by Equations 2.19 and 2.24; data from Makhor in and Kharchenko (1964). for Run 20 to be lying somewhere between the data for 300°C and 500°C. Molerus and W i r t h (1997) have used data from Janssen (1973) obtained with quartz sand (dp = 0.58mm) in air (horizontal tube) to illustrate the accuracy of their correla- tion 2.19. The results are shown in Figure 6.27 for various bed temperatures. As can be seen, at a 400 °C bed temperature and a particle size of dp = 0.58 m m , a max imum heat Results and Discussion 85 transfer coefficient close to /JO=400 W / m 2 - K has been measured. Now, it is well known that the heat transfer coefficient decreases wi th particle size in the regime of dp « 100 08 r I i 12 u-uraf[m/s] Figure 6.27: Experimental (symbols) with air at varying bed temperatures and predicted h0 (Equation 2.19); reproduced from Molerus and W i r t h (1997) wi th permission. Figure 6.28: Experimental and predicted h0>max (Equation 2.24) at different levels of temperature; reproduced from Molerus and W i r t h (1997) wi th permission. Results and Discussion 86 up to 1 m m . Figure 6.28 shows measured max imum heat transfer coefficients at 400°C for a particle size of d p=0.34 m m in the order of h0tmax « 5 0 0 W / m 2 - K . This suggests that our results for R u n 20 may be too low. Moreover, as seen i n Figures 6.24 and 6.25, the predicted m a x i m u m coefficient does not occur at the same gas velocity as for the experimental data. The prediction is st i l l increasing while the data is decreasing. Now, in both tests a loss of sand from the bed was observed for the highest gas flowrate. The premature decrease in h0 may be attributed to a reduction in the heat flow caused by this loss of sand. This behavior may not occur when using a more narrow particle size range as is generally the case for the data used to derive such correlations. W i t h a wide particle distribution such as used here (Figure C . l ) , the fine particles may be entrained while this is not the case wi th a narrow size range. Table 6.10 contains the measured and predicted max imum heat transfer coefficient, h0,max and h0%max respectively, using the correlations given i n Chapter 2. It can be seen that al l correlations point to the fact that a higher value for h0}Tnax would have been expected for both runs. This may be partly attributed to some error i n the temperature measurement as explained above. Also , according to Figures 6.24 and 6.25 it is clear that h0^nax occurs at a higher gas velocity than in the measurements. This may be due to the loss of sand during the measurement which may not occur when a narrow size distribution is used. Table 6.10: Measured, and predicted h0t,nax from various correlations for Runs 16 and 20. Run no. Measured Zabrodsky Varygin et al. Grewal and Saxena Molerus 16 449 641 572 698 651 20 336 518 464 568 531 Final ly, it is interesting to consider the instantaneous heat transfer coefficient, h,nst. Mickley et al. (1961) reported values at a point on a 6.35-mm tube located along the axis of a 0.1-m fluidized bed of 43-320 /.an particles and found sharply varying values, as shown in Figure 6.29. Baskakov et al. (1973) also obtained similar data. K u n i i and Levenspiel (1991) saw this behavior as evidence for the fact that the exchanger surface is Results and Discussion 87 bathed alternately by gas bubbles (very low hinst values) and by emulsion packets (high hinst values). The relatively high magnitude of the noise in our thermal fouling data may be attributed to this phenomenon. Microspheres, U =0.086 m/s Glass beads, U =0.186 m/s o 600 1500 cV 1000 » 500 Figure 6.29: Instantaneous h on a vertical tube; adapted from Mick ley et al.(1961). 6.3.2 Clean Coefficient For The Oil The heat transfer between a pipe and the fluid flowing wi th in it is determined either singly or i n combination by two mechanisms, namely, forced convection and natural convection. In most process plant heat exchangers where the fluid is pumped through the system at relatively high velocity, the effects of natural convection are, therefore, insignificant. In laminar flow, the distances required to attain the fully developed thermal boundary layer (thermal entry length, LeT) and hydrodynamic boundary layer (hydrodynamic entry length, Le) are given by: vfd,T 'fd,H = L Dt 0.05RePr O.ObRe (6.17) (6.18) lam For our test section wi th a non-heated entry length of about 40 cm, it was possible to treat the velocity profile as fully developed throughout the thermally developing region. Moreover, the Graetz number, defined as Gz = — RePr x (6.19) Results and Discussion 88 is an important parameter in the analysis of developing boundary layer phenomena. The thermal boundary layer is fully developed when Gz~x has a value of about 0.05, which is the origin of Equation 6.17. Correlations wi th a fully established velocity profile for a developing temperature boundary layer (Gz~x < 0.05) were compared wi th our ex- perimental results obtained i n Runs 16, 20, and 23. These correlations have usually been derived on the basis of constant fluid properties and the mean fluid temperature, Tb = (Tb,in + Tfc i 0 u t ) /2 , was used in calculating the nondimensional parameters. Gnielinski (1983) proposed the following Nusselt number (Nu = hi • Di/ki) based on the average heat transfer coefficient over the length 0 to x for a uniform wall temperature Nu = lMGz1/3 Gz > 10 3 (6.20) For the constant surface temperature condition, Kays (1955) presents a correlation which presumes a thermal entry length and is of the form TT- n „ 0.066S(Di/L)RePr ,„ n ^ where L is the heated length of the test section. The best results were obtained from a correlation proposed by Obot et al . (1997) who reported heat transfer data in laminar flow for the 0.7 to 126 Prandt l number range: ?Vu = 0.0086#e 3/ 2 i^-j^ Pr0A (6.22) From the knowledge of the measured heat transfer coefficient i n the fluidized bed, hQ, of the wall resistance, and of the overall coefficient, U0, the inside heat transfer coefficient, hi, was calculated. Equation 6.22 was used to predict the average heat transfer coefficient inside the tube, hi, and the results are given in Tables 6.11 and 6.12. The values of heat capacity and thermal conductivity required i n the calculation of the P rand t l number were obtained from Cassis et al. (1985) and Perry and Green (1984) respectively. It is shown that the flow is laminar and there is a fully developed hydrodynamic boundary layer with a developing temperature boundary layer over the whole length of the 46-cm heated section. Table 6.12 indicates that there is a significant deviation between experimental and predicted hi, especially for R u n 20. Now, i f we use the correlation 2.19 proposed by Molerus et al . (1995) to calculate h0, we can deduce the heat transfer inside the tube, Results and Discussion 89 Table 6.11: Parameters involved i n the calculation of hi. Run no. Tb Xfd,T Xfd.H Re Pr Gz~ l x 103 ( ° C ) ( c m ) ( c m ) 16 303 934 12 465 78 2.43 20 132 326 7 266 47 6.96 23 376 1073 22 824 49 2.26 Table 6.12: Measured (hi), and predicted (hi) coefficient from Equat ion 6.22. Run no. hi hi Dev. hitM Dev. ( W / m M < ) ( W / m 2 - K ) (%) ( W / m 2 - K ) (%) 16 498 408 22 451 11 20 530 252 110 293 16 23 407 444 -8 460 3 knowing the overall heat transfer coefficient UQ. The results, given in Table 6.12, become much more consistent wi th the predicted h{. This reinforces the validi ty of Molerus's correlation and the possibility of an error in the wall temperature measurement. Final ly, Table 6.13 gives the inverse overall heat transfer coefficient based on the external surface area of the test section, l/UQ, and the relative importance of each of the individual resistances wi th respect to the total resistance. The relatively high resistance from the fluidized bed (average=38% of the total) may reduce the sensitivity of the fouling unit to detect a change in the overall heat transfer coefficient that would result from fouling. Table 6.13: Total , and fractional tube side and shell side resistances 1. Total Tube/Total Shell/Total Run no. W~L x 103 Aol{AihiMVZ x) I/CIOMUO 1) 16 4.703 0.56 0.43 20 6.024 0.67 0.32 23 4.258 0.61 0.39 (W/m 2 -K); 'Tube wall resistance is less than 1% in these runs. Results and Discussion 90 6.4 Analysis of Variations in Fluidized Bed 6.4.1 Power Spectral Density In order to identify undesirable oscillations in process variables, their frequency, their relative importance, and their effects on the fouling data, the measurements were decom- posed by using a Fourier method called Fourier transform ( F T ) . For a signal that is both discrete and periodic, the appropriate transform is the discrete Fourier transform ( D F T ) . The D F T of the sequence {xt}, t = 0 , 1 , . . . , N — 1 is given by N - 1 X(n) = J2xtWNnti n = 0 , 1 , . . . , N - 1 (6.23) t=o WN = exp^j^j (6.24) This material is covered in many textbooks on digital signal processing such as Roberts and Mul l i s (1987). The D F T was computed using a fast algorithm implemented in M a t l a b © called fast Fourier transform ( F F T ) . The frequency content of a signal yt can be estimated from a periodogram Sp(6) which is an estimate of the power spectral density Sp(8). In practice, only a sample of the entire periodogram is computed. A set of equally spaced samples of Sp(6) can be obtained from the F F T algorithm for the D F T . Let N > L be a power of two, and let 60 = 2ir/N. Then SP(ne0) = \\Y,y^-3tn6a\2 = j\T,*tW^\* = ^j^- (6.25) t=o t=o where xt = ytwt, 0 < t < L - 1 (6.26) = 0, L < t < N - 1 wt = 1, 0 < t < L - l (6.27) = 0, otherwise This tool was applied to al l experiments and the results for R u n 5 are given in F ig - ure 6.30 as an example, plotted up to the Nyquist frequency. In Runs 3 to 7, a periodic Results and Discussion 9 1 variation in the air flowrate fluidizing the bed was observed, although its origin had not yet been identified. This resulted in oscillations of several process variables such as the temperature of the air entering the fluidized bed, T a t r , the fluid bed temperatures, and the heat flow. This is shown in Figure 6.30 by the major peaks at around 0.1 and 0.2 r ad /min . The period (p = 2ir/6 min.) corresponding to the first and second peaks was calculated and the results are given in Table 6.14. It can be noticed that, for a given run, the major fluctuations all have the same period, whose origin was the air building compressor as w i l l be shown later. Also, the air flowrate had at least two important oscillations whose frequency varied from run to run. The variation i n the air flowrate caused a corresponding variation in the heat transfer coefficient i n the fluidized bed as discussed in the last section and as a result, the heat flow fluctuated. The temperature measurements at the top and bottom of the fluid bed were usually more affected than (a) (b) 15 E 2 10 D) O •a p <D 5 0- 15 E 2 10 a> o •a o <5 5 C L 100 E 2 % 50 o <u CL T, lop •: . L... 11.1 i 0.2 0.4 (c) 0.6 0.8 mid 1 j k WM w ; \ 0.2 0.4 (e) 0.6 0.8 Tbot 0.2 0.4 0.6 Frequency, rad/min 0.8 0.08 £ 0.06 co o> % 0.04 o 0 ) a. 0.02 — AT b . . . i 7\A 0.2 0.4 (d) 0.6 0.8 200 E 150 CO •8 100 o •c CD D_ 50 E CO % 0.5 o CD CL "'"air , J D 0.2 0.4 0.6 0 X 1 0 " 3 (0 Heat Flow 0.2 0.4 0.6 Frequency, rad/min 0.8 Figure 6.30: Samples of the periodogram obtained from the F F T (Data from R u n 5). Results and Discussion Table 6.14: Magnitude and period of the peaks identified in Runs 3 to 7. Tair Q Ttop Tb ot Run T Mag. T Mag. x 10" T Mag. T Mag. T Mag. no. (min) (°c 2) (min) (kW2) (min ) (°c 2) (min) (°c 2) (min) (°C 2) 3 37 92 38 1.05 37 31 26 3 36 22 4 73 352 72 4.56 71 5 22 4 73 319 36 102 36 1.87 32 2 31 1 36 80 5 67 195 67 8.60 67 13 144 6 67 86 32 26 32 2.83 32 3 33 8 31 15 6 66 212 66 9.90 66 8 65 6 65 45 32 35 32 1.99 32 5 30 8 32 14 7 61 42 62 1.67 24 1 34 3 53 1 53 74 53 1.26 - - - - - - the middle temperature as shown in Figure 6.30 and Table 6.14. Also , the second peak was not significant for all the runs. It is interesting to note that the fluctuation in heat flow may not be detected from the fluid bed temperature measurements as shown by R u n 7 and others. Final ly , after R u n 8 the fluctuations i n air flowrate were reduced and no other significant oscillations were detected. 6.4.2 Elimination of Fluctuations To reduce the effect of air flow oscillations on fouling data, two approaches were taken. In the first one, a band-stop filter was designed specifically to remove the major oscillations from the data and in the other approach, the effect of the fluctuations was minimized. In the discussion of filters, signals are viewed as a collection of signal components with different frequencies. A filter is designed to accept certain frequencies and reduce other frequencies. The Bode diagram indicates which frequency components the filter reduces and how much each component is reduced. In this section, the design and application of a band-stop filter to eliminate the fluctuations discussed previously are demonstrated. A band-stop filter has two frequency values, called the half-power frequencies, that are separated by a frequency range called the bandwidth of the filter. The band-stop filter Results and Discussion 93 reduces al l components of the signal between the two half-power frequencies and does not affect the components on either side. The max imum reduction of the signal occurs at the midpoint between the two half-power frequencies. A second order digital Butterworth filter is of the form n H J 1 + aiq~l + a2q~2 V ' where q~x is the backward-shift operator and the parameters determine the frequency band to be attenuated and the attenuation. The function 'But ter ' in M a t l a b © was used to design the filter; the inputs of the function were the order of the filter (=2) and the two half-power frequencies, whereas the outputs were the parameters a and b. To reduce the two significant components identified in last section, two band-stop filters were designed. The Bode diagram for the digital filter used to minimize the component occurring at around 0.1 r ad /min in R u n 5 (see Figure 6.30) is shown in Figure 6.31. The filter produces -50.9 dB of attenuation at the desired frequency of 0.0939 r ad /min . Table 6.15 contains fx (T ! 1 U J ; ; ; . — ; — 10"1 10° Frequency, rad/min 1001 : : 1 Frequency, rad/min Figure 6.31: Bode diagram of the band-stop filter used to reduce oscillations in R u n 5. the parameters a and b for the two filters used i n Runs 5 and 6. The data for the temperature difference across the test section were filtered unt i l sufficient attenuation of the desired components was obtained. The resulting power spectral density estimate for ATb in R u n 5 is shown in Figure 6.32 which clearly shows the attenuation of the two components. The heat flow was recalculated using the filtered data and the results are Results and Discussion 94 Table 6.15: Parameters for the bandstop filters for Runs 5 and 6. Run no. Filter 1 6l &2 63 CJl 02 5 0.9629 -1.7177 0.9629 -1.7177 0.9258 6 0.9651 -1.7149 0.9651 -1.7149 0.9302 Filter 2 5 0.8616 -0.9239 0.8616 -0.9239 0.7232 6 0.8632 -0.9351 0.8632 -0.9351 0.7263 (a) Raw data. (b) Filtered data. 0.08 0.06 £ 2 D ) O T J 0.04 . O CD C L 0.02 0 1 1 1 1 0.2 0.4 0.6 Frequency, rad/min 0.8 0.08 0.06 E CO D ) O T3 0.04 . O CD Q_ 0.02 1 1 1 I * ... 0.2 0.4 0.6 Frequency, rad/min 0.8 Figure 6.32: Samples of the periodogram for the raw and filtered AT), for R u n 5. illustrated in Figure 6.33 for Runs 5 and 6. The attenuation of the two major oscillations has clearly improved the quality of the fouling data. The air flowrate variations were caused by the periodic pressure increase and decrease of the air building compressor occurring at each cycle of the compressor. The variability in the frequency of this cycle observed in Table 6.14 depended on the demand of air at the time of the experiment and was sometimes decreasing during the night time within the same run. To minimize the effect of this cycle on the air flowrate, the pressure of the air regulator was reduced from 60 to 40 psig. A test revealed that when the pressure was set at 60 psig, the pressure varied between 50 to 60 psig wi th in one cycle of the compressor. Because the compressor could not provide a constant pressure of 60 psig, the pressure of the air regulator was reduced to 40 psig. The effect of this change on the Results and Discussion 95 air temperature entering the fluidized bed, which is directly related to the air flowrate, is shown i n Figure 6.34. No significant oscillation in air flowrate was observed after implementing this change. (a) Run 5 (raw data). (b) Run 6 (raw data). 0.55 0.5 0.45 d 0.4 0.35 500 1000 Recirculation time, min (c) Run 5 (filtered data). 0 500 1000 Recirculation time, min 0.55 0.5 0.45 d 0.4 0.35 0.55 0.5 0.45 d 0.4 0.35 r 0 500 1000 Recirculation time, min (d) Run 6 (filtered data). 500 1000 Recirculation time, min Figure 6.33: Raw and filtered heat flow for Runs 5 and 6. 300 o v 2 5 0 200 Air temperature versus time. i ! i ! ! Air pressure= 40 psig i - 1 psig i i 'I- Air pressure= 50 - 60 i 200 400 600 800 1000 Time, min 1200 1400 1600 1800 Figure 6.34: Test revealing the effect of air pressure on air temperature, Tair. Results and Discussion 96 6 .4 .3 Sensitivity of U0 to Air Flow Variations According to Equations 2.2 and 2.4, the heat flow and the overall heat transfer coefficient, /7 0, share a similar dependency wi th the air flowrate as the heat transfer coefficient between the bed and the test section, h0. The semi-empirical knowledge of h0 as a function of the superficial gas velocity described in Section 6.3.1 could be used to estimate changes in U0 resulting from air flowrate variations using Equation 2.4. Unfortunately, in none of the runs was a continuous measurement of the air flowrate recorded. Also , the correlations used in Section 6.3.1 could not predict the max imum in the curve hQ vs. excess gas velocity as observed experimentally. Concerning the experimental data for h0 obtained in Runs 16 and 20, they are valid only for the conditions under which they were obtained. The heat flow generated in each run depends on several factors as seen previously. Because the purpose of this work was not to study heat transfer in a fluidized bed, many of these parameters were not controlled from run to run. Nevertheless, i n order to have an idea of the sensitivity of U0 to air flow variations, other empirical relationships between the experimental data were sought. As seen previously, a relationship was observed between the air flowrate and the temperature of the air entering the fluidized bed, Tair. One approach considered was to estimate air flowrate variations based on this relationship and on the knowledge of T a t>. Runs such as 5 and 6 would have provided a relationship between Ua and T a i r and R u n 20 would have given the l ink between T a i> and air flowrate. However, this approach was not valid since it was found in R u n 18 that T a , r was also affected by variations in line voltage. Another approach for evaluating the sensitivity Ua to air flowrate variations was to relate the fluid bed temperatures to U0 by using the data obtained in R u n 20 as a result of step changes in air flowrate. The correlations found between U0 and the three fluid bed temperatures obtained in R u n 20 are shown in Figure 6.35. The data indicate that an increase in air flowrate causes an increase in the temperature of the bed at the bottom and a decrease of the bed temperature at the top, but does not affect the temperature of the bed in the middle. Results and Discussion 97 180 * 160 JS 140 3°120 100 h Overal heat transfer coefficient vs. fluid bed temperatures during step changes in air flowrate. 1 — i 1 1 " — ! 420 180 h * 160 O J E 5= 140 180 * 160 g 140 3°120 100 390 O 0 :0 Air rotameter = 5.5a O 0 OC© : Q Air rotameter = 8.0 440 460 480 T. 500 520 540 1 1 o <§po° o r 1 ! 1 § S P ' O 0 O O fP O c I ! ! o : cp O Co . OfO: OP Qj 0 o o • • - C D : °o: ° ''[6Q>0 O O • o" i i i i i i 1 1 1 1 425 430 435 440 445 450 455 460 465 470 475 T mid 0:Q§^30@6o 0 0 C P 0 O O f J o O O O 0 0 0 0 O 0 0 # . O ^ : Air rotameter = 8.0 P CD ^SE©' o Air rotameter = 5.5 400 410 420 430 Tbot 440 450 460 470 Figure 6.35: Correlation between U0 and the fluid bed temperatures in R u n 20. 6.5 Tests W i t h a Known Fouling Fluid In order to evaluate the abili ty of the fouling unit to detect fouling, Runs 19 to 21 were performed using a mixture of fuel oi l (75%wt.), heavy oi l (10%wt.), and deasphalted o i l — DAO—(15%wt . ) . This blend was selected because of the high fouling rates measured when used in another fouling unit (A l -A ta r (2000)). The results obtained are discussed by taking into account all the fouling runs performed in the present work. For each run, the in i t ia l and final values of the process variables believed to affect the heat flow to the test section were calculated by taking an average of twenty-one points. The ini t ia l value was calculated after a steady-state regime was achieved in al l measured variables. In order to estimate the uncertainty in the measured and calculated variables, a linear regression (LS) was performed through these twenty-one points. Assuming the Results and Discussion 98 prediction errors to be 7V(0, <7 2), a 95% confidence interval was obtained as follows ) (6.29) where ape is the standard error of the prediction errors and (tvaiue) is obtained from a Student's t-distribution table. The results are given in Table 6.16 where the subscripts 0 and / refer to initial and final respectively and where N is the number of data points used to obtain the values. Table 6.16: Initial and final values of measured and calculated variables for all runs with 95% confidence interval (CI). Run datao data; N CI l/Uo,/ CI Qo Qf no. (min) (min) (m 2-K/kW) (m 2-K/kW) (kW) (kW) 1 240-400 1390-1560 18 4.4 0.3 6.8 0.6 0.64 0.45 2 200-300 630-730 12 5.3 0.7 5.4 0.3 0.40 0.39 3 270-370 671-770 21 6.3 0.6 6.3 0.6 0.36 0.36 4 216-316 1185-1305 21 4.1 0.2 4.9 0.2 0.40 0.33 5 101-201 862-962 21 4.2 0.3 4.3 0.4 0.46 0.44 6 125-225 957-1057 21 4.4 0.3 4.5 0.4 0.45 0.43 7 110-210 787-887 21 4.3 0.2 5.0 0.3 0.48 0.41 8 100-200 546-646 21 5.7 0.3 5.8 0.4 0.34 0.33 9 100-201 817-917 21 4.7 0.3 4.7 0.2 0.42 0.42 10 75-176 662-762 21 4.6 0.1 4.6 0.1 0.43 0.43 11 90-191 865-956 21 4.7 0.2 5.1 0.2 0.42 0.39 12 100-200 661-762 21 4.8 0.3 5.2 0.2 0.39 0.37 13 115-216 1023-1123 21 3.7 0.1 3.8 0.2 0.75 0.73 14 231-331 1048-1148 21 4.4 0.1 4.2 0.1 0.63 0.65 15 200-301 1909-2009 21 4.9 0.3 4.7 0.3 0.56 0.59 16 355-455 1022-1122 21 4.7 0.2 5.2 1.1 0.62 0.59 17 301-401 3186-3287 21 4.6 0.1 4.5 0.1 0.59 0.61 18 501-602 3253-3353 21 4.5 0.2 4.2 0.2 0.51 0.54 19 166-266 1203-1304 21 6.8 0.2 7.5 0.4 0.19 0.17 20 200-301 1788-1889 21 5.9 0.2 5.9 0.1 0.50 0.49 21 200-301 1919-2019 21 4.5 0.1 4.6 0.1 0.66 0.64 22 201-301 1654-1754 21 4.4 0.2 4.0 0.1 0.50 0.58 23 201-301 1153-1254 21 4.3 0.1 4.2 0.2 0.51 0.53 Results and Discussion 99 According to these results, the change in (1/U0) is significant for Runs 1, 4, 7, and 19. Section 6.2.3 has shown that for Runs 1, 4 and 7, the change in heat flow was mostly due to a variation in liquid flowrate. Runs 19, 20, and 21 were performed with the DAO mixture. For Run 19, there was no significant change in all the measured variables. This is the only run where both the increase in (1/U0) was significant and where there is no indication of significant changes in process variables. Figure 6.36e indicates that the mass flowrate during Run 19 was constant while the heat flow was slightly decreasing (see Figure 6.36a). The results of this run therefore suggest fouling formation. For Run 20, Table 6.15: Continued. Run Ttop,o CI Ttopj CI Tmid,0 CI Tmid,f CI Tbot,o CI Tbotj CI no. (°C) (°C) CC) (°C) CC) (°C) CC) (°C) CC) (°C) CC) (°C) 1 534 16 569 12 491 2 490 0 - - 2 533 25 528 18 496 7 497 3 - - 3 510 9 509 8 496 6 498 4 477 10 480 9 4 508 4 509 5 504 8 506 7 435 16 429 20 5 507 10 510 9 501 7 502 9 490 15 484 15 6 507 5 509 6 501 7 503 8 500 13 499 12 7 511 3 511 4 502 7 501 7 510 7 509 6 8 505 3 507 4 498 7 502 7 486 8 488 11 9 506 5 506 4 499 6 501 5 505 8 503 12 10 503 4 502 3 500 5 499 6 502 5 501 8 11 504 3 505 4 498 4 500 5 503 6 502 8 12 505 2 505 4 500 6 500 4 501 5 499 5 13 601 7 605 5 594 7 596 6 603 13 601 14 14 601 5 603 4 596 6 597 4 596 12 593 9 15 528 11 537 6 503 8 504 5 483 13 489 12 16 622 7 669 83 602 8 605 5 611 11 602 17 17 617 9 627 10 599 10 592 10 587 9 581 7 18 594 8 593 5 597 10 598 14 598 9 594 8 19 246 6 246 6 248 5 249 13 222 5 219 9 20 450 5 447 5 448 8 448 9 453 12 447 14 21 445 5 447 6 445 12 444 13 441 8 436 6 22 610 5 613 6 614 9 610 7 616 13 612 6 23 613 4 618 3 610 4 610 5 615 3 620 4 Results and Discussion 100 there is no significant change between the initial and final heat flow—this is also true for the flowrate as shown in Figure 6.36e—although some variations occurred during the run (see Figure 6.36a). The observed change in Q at around 700 min (Fig. 6.36a) is believed to have been caused by a decrease in bulk temperature which occurred at the same time; the bulk temperature came back to its original value at around 1000 min. Hence it was concluded that no fouling was detected in Run 20. For Run 21, the heat flow had an decreasing trend (Fig. 6.36b) although it was less pronounced than for Run 19. More fluctuations in flowrate were observed in Run 21 than in Runs 19 and 20 (Fig. 6.36f). Table 6.15: Continued. Run no. mo CI (g/s) (g/s) m/ CI (g/s) (g/s) Ti„, 0 CI CO (°C) Tin,/ CI CO cc) 1 - - 196.9 0.6 195.4 1.8 2 - - 277.4 0.6 275.8 0.5 3 - - 244.9 0.5 245.1 0.6 4 - - 284.7 0.4 286.4 0.6 5 - - 288.5 0.8 288.9 0.9 6 - - 289.4 1.0 289.5 0.8 7 - - 276.5 0.5 278.3 0.7 8 31.1 0.6 30.8 0.5 290.5 0.3 291.3 0.3 9 13.7 0.1 13.1 0.1 283.9 0.4 284.6 0.2 10 9.3 0.5 9.1 0.1 277.7 0.4 277.9 0.2 11 10.4 1.0 10.1 0.7 280.9 0.6 282.5 1.0 12 8.4 1.9 7.8 1.1 286.0 0.8 285.7 0.6 13 15.1 0.1 15.8 0.2 288.5 0.7 289.1 0.5 14 7.5 0.5 7.7 0.3 282.8 0.4 282.5 0.3 15 16.3 0.4 16.3 0.1 198.8 0.4 198.9 0.2 16 7.3 0.7 7.6 0.1 286.4 0.6 285.7 1.4 17 7.6 0.0 7.7 0.0 286.7 0.5 286.3 0.5 18 6.6 0.1 6.5 0.0 330.3 1.4 330.8 0.9 19 5.8 0.0 5.8 0.0 86.5 0.2 86.5 0.2 20 3.2 0.0 3.2 0.0 95.0 0.3 93.8 0.2 21 12.8 0.5 12.7 0.2 106.7 0.3 106.8 0.2 22 8.4 0.1 8.3 0.4 361.4 0.5 343.2 0.6 23 7.8 0.3 8.0 0.3 363.8 0.5 361.9 0.6 Results and Discussion 101 The test section used in Run 19 was cut axially in order to examine the inner surface of the tube by visual inspection. Only a layer of oil was observed; the layer was thin (a) Heat flow calculated with actual flowrate vs. t. 0.5 0.45 0.4 § 0.35 Q > 0.3 0.25 0.2 0.15 1 •—1 1 " 1 Run 19 Run 20 0 500 1000 1500 2000 (c) 1/U calculated with actual flowrate vs. t. 0 500 1000 1500 2000 (e) Mass flow vs. t. 6 5.5 -S 5 £ 4.5 w in ( 0 S 4 3.5 3 Run 19 Run 20 500 1000 1500 2000 t, min r (b) Heat flow calculated with actual flowrate vs. t. 0.8 r 0.75 0.7 0.65 > 0.6 O 0.55 0.5 0.45 \ Run 21 500 1000 1500 2000 (d) 1/U calculated with actual flowrate vs. t. 5.5 § 5 34.5 4 3.5 ( 14 13.5 13 Dl 5 §: 12.5 ( 0 m to 2 12 11.5 11 Run 21 Run 21 500 1000 1500 2000 (f) Mass flow vs. t. 500 1000 1500 2000 t, min Figure 6.36: Heat flow, (l/U0), and mass flowrate in Runs 19 to 21. Results and Discussion 102 enough such that the surface of the tube could st i l l be seen. No black and thick deposit such as that obtained wi th the probe of the other unit when used wi th the same mixture was found. For Runs 20 and 21, the test section was washed wi th varsol according to the procedure described in Chapter 5 in order to measure wc, the amount of coke in the test section at the end of a run. The results are given in Table 6.17. Note that wc could Table 6.17: Coke collected in test section at the end of Runs 20 and 21. Run no. (mg) 19 - 20 41 21 18 not be measured in R u n 19 because of the tube opening performed. Since the amount of insolubles in the D A O blend is probably negligible, the mass of coke for Runs 20 and 21 is therefore the result of fouling. However, based on the thermal measurements obtained in Runs 20 and 21, these deposits were apparently too small to be detected by the fouling unit. Note that the higher amount collected in R u n 20 might have been caused by a lower l iquid velocity, given that the other process variables and the total recirculation times were very similar (see Table 6.1), since fouling is often expected to increase when the velocity decreases. The thermal measurements of R u n 19 indicate fouling formation. Now, for the runs with pitch and C H G O , the mass deposition measurements have shown the absence of significant fouling under the conditions covered. However, in some of these runs, varia- tions i n 1/U0 were observed, although they could not be explained in terms of flowrate variations. Because of that, and since no mass deposition measurements were made in R u n 19, which was the only run where fouling seems to have been detected, the evidence is judged insufficient to say whether fouling was actually formed in R u n 19. For Runs 20 and 21, some fouling has occurred as shown by the measured deposits, but detection by thermal measurement may have been prevented by the small amounts measured, and by the noise level and variability of the fouling unit present in all the other experiments. Chapter 7 Conclusions &: Recommendations 7.1 Conclusions The main objective of this study was to evaluate the tendency of the pitch-coker heavy gas oil stream to form coke as well as to assess the abil i ty to detect it under the appro- priate bulk and surface temperature conditions. To meet this objective, several fouling experiments were done by recirculating a 50:50%vol. pitch-heavy gas o i l blend over 11-56 hour periods wi th bulk fluid temperatures of 200-375°C, tube side velocities of 0.3-2.2 m/s , and fluid bed temperatures in the range 500-615°C. F low was generally laminar. Both the mass deposition and thermal measurements showed no significant fouling by coke formation. Interpretation of the thermal fouling data was sometimes made difficult by their sensitivity to variations in process variables. B y the use of different data analy- sis techniques and of empirical correlations found between process variables, fouling was distinguished from other effects. In order to see whether the absence of fouling observed was due to the fouling unit or could be attributed to the nature of the test fluid used, a series of fouling experiments were performed wi th a blend of de-asphalted oi l known to give measurable fouling rates in turbulent flow and in similar periods of time as for the coking experiments. Moreover, viscosity and density measurements were done to determine the flow regime in the fouling runs and to account for possible viscosity changes during the fouling exper- iments. Addi t iona l experiments were performed to monitor the viscosity change during recirculation of the test fluid and also the change in the amount of toluene insolubles in the 50:50%vol. pitch-heavy gas oi l blend. Final ly , measurements of heat transfer co- efficients were also made to estimate the relative importance of the thermal resistances between the fluidized bed and the bulk l iquid. 103 Conclusions & Recommendations 104 Based on these studies, the following conclusions can be drawn: • A n improved insulation of the fouling unit and the use of heating tapes increased the capability of the unit to handle viscous fluids and to reach the higher bulk temperatures required (see Sections 4.7.1 and 4.7.3). • As described in Sections 4.2 to 4.4, the design and implementation of a pressure drop measuring system combined wi th a digital balance setup provided an accurate mass flowrate measurement of viscous fluids using a small amount of test fluid. • A n adjustment of the air pressure regulator reduced undesirable oscillations in air flowrate as shown in Section 6.4.2, thereby improving both the fluid bed temperature profile and the thermal fouling data. The data obtained prior to this adjustment were improved by filtering through a digital band-stop filter as demonstrated in Section 6.4.2. Oscillations in the voltage to the air preheater were also reduced by use of a voltage regulator. • From the viscosity measurements reported in Chapter 3, viscosity-temperature cor- relations were developed over a wide range of temperatures for the viscosity pre- diction of any blend of pitch and C H G O . Density-temperature equations were also derived from the density data presented in the same chapter. Hence a laminar flow regime in a l l the fouling experiments performed could be determined. • In some fouling runs a drop in viscosity was observed and a possible bias effect on the mass flowrate measurement was demonstrated in Section 6.2.5. • For the runs with the 50:50%vol. p i t c h - C H G O blend, the TI measurements are consistent with the previous work of Watkinson et al . (1998) as discussed in Sec- tion 6.1.2; i.e. as long as a certain amount of volatiles has not been released, no significant change in the TI of the test fluid wi l l occur. • In Sections 6.2.1 and 6.2.2, the use of cross correlation analysis and empirical correlations found between process variables confirmed the effect of l iquid flowrate variations on thermal measurements. A n A R M A model and a variable flowrate approach were applied to the measurements which essentially eliminated the effect Conclusions & Recommendations 105 of l iquid flow variations as discussed in Section 6.2.3. Also , the configuration of the bypass circuit was modified thereby eliminating the variations i n l iqu id flowrate (see Section 6.2.4). • The tests for determining the heat transfer coefficient revealed the complexity of heat transfer in fluidized beds. Comparison of the data wi th predictions from correlations in Section 6.3.1 indicated that the wall temperature measurements may not always provide the actual wall temperature. Moreover, the loss of sand from the bed may explain the fact that the measured maximum heat transfer coefficent occurs at a lower gas velocity than for the predicted coefficient. The premature decrease in h0 may be attributed to the relatively large particle size range of the sand used. • In Section 6.3.2 the measured and predicted heat transfer coefficients inside the test section have shown the relative importance of each of the individual resistances between the bed and the bulk fluid wi th respect to the total resistance. The resis- tance i n the bed was as high as around 38% of the total resistance; this may reduce the sensitivity of the fouling unit to detect a change in the overall heat transfer coefficient that would result from coke deposition. • Over the range of bulk fluid temperatures (200-375°C) , fluid bed temperatures (500-615°C) , and l iquid velocities (0.3-2.2 m/s) , no fouling was observed over recir- culation periods of 11-56 hours. A statistical analysis of the thermal measurements on the 50:50% vol . p i t c h - C H G O blend presented in Section 6.5 showed that all the significant variations observed in the inverse overall heat transfer coefficient could be explained by variations in process variables. The analysis of the mass deposition measurements given in Section 6.1.3 also suggested evidence of very small coke for- mation over the range of conditions covered. Calculations of an equivalent l iquid thickness of a residue layer presented in Section 6.1.3 revealed that the amounts of coke in the test section measured in the runs performed wi th adequate fluid bed cooling may have come exclusively from this residue layer. As for the other exper- iments, it was concluded that the coke collected was formed as a result of batch coking reactions in the residue left on the tube wall due to inadequate cooling of the fluid bed. Conclusions & Recommendations 106 • For the tests wi th the DAO blend, the mass deposition measurements indicated that some fouling has taken place in Runs 20 and 21, although it was not detected from the thermal measurements. In R u n 19 the thermal data indicated significant fouling. However, no mass deposition measurement were made, hence the evidence is judged insufficient to say whether fouling actually occurred. Nevertheless, based on the observed noise level and the variabil i ty i n process variables, and the magnitude of the thermal resistance of the fluid bed, it is clear that the abil i ty of the fouling unit to detect deposit formation must be improved. 7.2 Future Work Based on the results obtained, the following recommendations are suggested to verify and ensure that the fouling unit is able to form and detect fouling and to provide more insights into the precipitation of carbon-rich material from heating heavy petroleum streams: • As discussed in Section 6.3.2, the high thermal resistance due to the fluidized bed may be detrimental to the sensitivity of the fouling unit to detect coke formation. Also, the high level of noise observed in the thermal measurements deteriorates the quality of the data and appears to be due to the intrinsic nature of the fluid bed as suggested in Section 6.3.1. Moreover, the heat transfer between a fluidized bed and a vertical tube is extremely complex and the experiments revealed the difficulty of maintaining a constant heat flow to the test section, which is essential for a correct interpretation of the fouling data. Hence it seems appropriate to consider another heating method. • It is recommended to use a 'Portable Fouling Research Uni t ( P F R U ) ' probe capable of reaching the desired surface temperatures and which is supplied by 'Heat Transfer Research Incorporated ( H T R I ) ' because of the successful results obtained wi th this type of probe in an apparatus originally constructed by Fetissoff (1982). It has several advantages over the fluidized bed. The thermal resistance between the probe surface and the bulk l iquid is usually the dominant resistance as opposed to the fluidized bed. Also, it is experimentally much simpler to use because of the fewer Conclusions & Recommendations 107 operations required to replace the probe and because the heat flow is self-controlled. Due to its design the surface temperature is readily obtained and is l ikely to be more accurate than the more difficult measurements in a fluid bed. Furthermore, the evidence of coke formation is more obvious since fouling occurs on the outer surface of the probe. • As explained in Section 6.1.2, the amount of toluene insolubles in the test fluid remains approximately constant as long as a cri t ical yield of about 30% has not been reached. It is important to operate under this value to keep the properties of the test fluid constant. A water condenser has already been installed i n the vent line of the feeder to return the condensates in the system. • Because of the change in viscosity observed in the experiments and its possible bias effect on the flowrate, it is recommended to monitor the viscosity and to ensure it remains constant during recirculation. • Due to the voltage variations observed, it is recommended to maintain the power to the unit constant by using voltage regulators when necessary. • Due to the flammable and toxic nature of the fluids studied and the long periods of t ime required by the fouling experiments, it is recommended to implement al l the necessary security devices. A n alarm system relating the pressure drop across the orifice plate to the total power to the unit has been designed and is now being used. This system shuts off the power in case the pressure signal becomes outside a specified pressure band. The above suggestions wi l l help ensure that whatever change observed in the overall heat transfer coefficient is due to fouling not to variations in process variables, in fluid properties, or to a problem in the design of the fouling unit. Once the abil i ty of the fouling unit has been confirmed—for example by repeating the tests wi th the D A O mixture—the coke forming tendency of various blends can be studied systematically by varying the fluid velocity, the bulk and surface temperatures, and the recirculation time. Bibliography Al-Atar, E. (2000). Effect of oil compatibility and resins/asphaltenes ratio on heat exchanger fouling of mixtures containing heavy oil. M.A.Sc. Thesis. University of British Columbia. Albright, L. F., B. L. Crynes, and W. H. Corcoran (1983). Pyrolysis: Theory and industrial practice. New-York: Academic Press Inc. Allan, J. M . and A. S. Teja (1991). Correlation and prediction of the viscosity of defined and undefined hydrocarbon liquids. Can. J. Chem. 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Heat transfer in fluidized beds: Convective heat transfer in fluidized beds. In J. F. Davidson, R. Clift, and D. Harrison (Eds.), Fluidization (2nd ed.)., pp. 437. Orlando: Academic Press Inc. Yue, C. and A. P. Watkinson (1998). Deposition of coke in heating of heavy hydrocar- bons, final report phase i . Technical report, University of British Columbia. Zabrodsky, S. S., N. V. Antonishin, and A. L. Parnas (1976). On fluidized bed-to-surface heat transfer. Can. J. Chem. Eng. 54, 52-58. Zuiderweg, F. J. (1967). Report. In A. A. H. Drinkenburg (Ed.), Proceedings of The International Symposium of Fluidization, pp. 739. Amsterdam: Netherlands Uni- versity Press. Appendix A Calibrations The calibration curves for the orifice plates are shown in Figures A . 2 and A . 3 for different operating temperatures. The numbers in parentheses in the upper figures refer to the run number while the numbers in the lower figures corresponds to the discharge coefficient values. The calibration curve for the fluidized bed air rotameter is given i n Figure A . l . Fluidized Bed Air Flowmeter Calibration Curve, Tube no. :B-250-6 / G l a s s Ball Rotameter Sca le (cm) Figure A . l : A i r rotameter calibration curve. 117 Calibrations 118 Orifice Plate 1/8" Discharge Coefficient Versus Reynolds Number (same blend). O 0.5^ ! ! '—r~ X X X > • - " * - ^ < _o - 0.590 . J i i I i i — 1 — ' •— I - J 103 104 Re Figure A . 2 : Orifice 1/8" calibration and discharge coefficient; symbols in lower graph represent same data as in upper graph; bulk inlet temperature indicated in legend of upper graph and R u n 8 indicated in parentheses. Calibrations 119 Orifice Plate 1/16" Calibration with a 50:50 %vol. Pitch/Coker HGO Blend. 1 1 1 1 1 — 1 i i m^a AP , a=0.52319E-04 + 0.17186E-05 (95% CL) • m2=b AP 1 / 2 , b=0.59136E-04 + 0.17409E-05 (95% CL) _i_ * * 286 °C (12) - o o 289 °C (13) X X 283 °C (14) • • 199 °C (15) - 0 0 286 °C (16) - V V 331 °C (18) m i 2 - 50 100 150 200 250 300 350 400 450 500 550 AP 1 / 2 (Pa) Orifice Plate 1/16" Discharge Coefficient Versus Reynolds Number (same blend). O 0.5 i 1 ! -[ j : n 6* o V b 0.636 0.697 v v 0.550 103 104 Re Figure A . 3 : Orifice 1/16" calibration and discharge coefficient; symbols in lower graph represent same data as in upper graph; bulk inlet temperature indicated in legend of upper graph and run number indicated in parentheses. Appendix B Properties of Fluids and Distillation T B P curves Table B . l : Properties of pitch and C H G O Parameter Pitch CHGO Carbon, wt.% 81.6 84.0 Hydrogen, wt.% 9.1 10.5 Sulfur, wt.% 5.3 4.3 Nitrogen, ppm 6557 3810 Aromatic Carbon ( C i 3 NMR), % 34.2 - MCR, wt.% 27.1 2.8 Ash, wt.% 1.5 - Density (25°C), g/mL 1.071 0.960 Ni, ppm 159 0.0 V, ppm 422 2.3 Table B.2: Some properties of Fuel O i l , Co ld Lake Heavy O i l and De-Asphalted O i l Parameter Cold Lake Heavy Oil Fuel Oil De-Asphalted Oil Saturates, wt.% 23.14 69.62 20.72 Aromatics, wt.% 49.84 27.71 68.45 Resins, wt.% 10.4 2.72 10.08 Asphaltenes, wt.% 16.63 Trace 0.76 Polars, wt.% 27.03 2.72 10.84 Carbon, wt.% 80.27 86.41 86.71 Hydrogen, wt.% 10.52 12.76 11.15 Nitrogen, wt.% 0.41 0.21 0.28 Sulphur, wt.% 4.51 0.56 3.54 H / C atomic ratio 1.57 1.77 1.58 120 SIMDIST 121 Figure B . l : SIMDIST for Virgin and Coker HGOs. Appendix C Size Distribution of Quartz Sand Used in Fluid Bed Figure C . l : Size distribution of quartz sand used in fluidized bed; mean particle diame- ter=0.34 m m . 122 Appendix D Sample Calculations D . l Tube Side Velocity, and Reynolds Number. For rhc = 9.2 x I O - 3 kg/s , D , = 5.33 x I O - 3 m , and p calculated at ¥ b = 287°C from Equation 3.2 (conditions of R u n 10): = = 0.48 [m/s] ( D . l ) p • irDf For the same R u n , wi th v calculated at Tb from Equation 3.9 where A , B , and C are given in Table 3.4 (51.7%wt. pitch and Dut t ) , the Reynolds number is: Rec = = 487 (D.2) v D.2 Heat Flow, Overall Heat Transfer Coefficient, and Thermal Fouling Re- sistance fTout(t) r Qv(t) = m(t) / CP(T) • dTb(t) [kW] (D.3) JTin{t) where Cp = (0.055 + 6.818 x 10" 3 • T(t) - 4.464 x 10~ 6 • T2) [ l d /kg -K] (see L u (1989)) and m is given by E q . 6.12. W i t h DQ = 6.35 X 10" 3 m and L = 0.46 m , the overall heat transfer coefficient at time t based on the actual mass flowrate is: Uo,v = n Q r v { t ) A T [m'-K/kW] (D.4) irD0L • Allm i A T {Ttop— Tout) — (Tbot — Tin) /n ,,\ where AT/, , , = —r— ——- (D.5) ln[(ltop - lout)/(Ibot - lin)\ The thermal fouling resistance is calculated as the difference between the reciprocals of overall heat transfer coefficients under clean conditions and at time t: 123 Sample Calculations 124 where UOiV(0) is an average of twenty-one points calculated from the S.S. value reported in Table 6.1. D.3 Superficial Gas Velocity, U, and Minimum Fluidization Velocity, Umf. 4 • Vn u = 7nf <D'7> where Db=0.05 m and Vg, the volumetric flowrate of air, is obtained by correcting the value read from Figure A . l for the appropriate conditions of pressure and temperature of the fluid bed. The m i n i m u m fluidization velocity is given by: 1.75 (dp • pg - U m f Y , 150 • (1 - emf) -dp-pg- U m f = d3p • P g • (p. - pg) • 9 ( . D.4 Experimental Bed-to-Wall and Oil Side Heat Transfer Coefficients. The bed-to-tube wall heat transfer coefficient measured in Runs 16, 20, and 23 was calculated from: 1 \ nDc-L-ATI^-1 U 0 , J Q v (Tt0p,w Tout) (Tf)ot,w ~~ Tin) (D.9) (D.10) A T / = m ln[{Ttop,w ~ Tout) — {Tbot,w — Tin)] where the subscript w refers to outer wall temperature. The tube side heat transfer coefficient measured was calculated according to: A0 • hi = 'TXDO • L • A T / m A0 • ln{D0/D,)' 2vr • L • k ( D . l l ) Sample Calculations 125 D.5 Effect of h0 on Sensitivity of Unit to detect Coke Formation. A l - A t a r (2000) obtained a fouling resistance of 0.3 m 2 - K / k W — f i n a l value—after recircu- lating a 75% F O / 1 0 % H O / 1 5 % D A O blend for 380 min . at an average bulk temperature of 85.5 °C , average surface temperature of 222 °C, and l iquid velocity of 0.75 m/s . What change in 1/U0 would result in our unit given this final value? The change in 1/U0 is calculated from \Uo,c J \Ai-hi + ^ + ho) and can be expected to be at least 10% i f evident detection is to be made. The subscripts C and F refer to clean and fouled conditions respectively. Table D . l gives the results for three values of h0, the heat transfer coefficient in the fluid bed. The value of 489 and 451 W / m 2 - K for hQ and /i, respectively are the predicted values for R u n 16. Table D . l : Effect of h0 on the change i n l / ( 7 0 . h0 hi Change in 1/Uo (W/m 2-K) (W/m 2-K) (%) 489 451 8 1500 451 11 3000 451 12 From these results it may be inferred that the sensitivity of the unit is rather low. Also, it is shown that as h0 increases, the change in l / ( 7 0 becomes more significant. A l - A t a r (2000) reported a value of (1/(7 C)=0.317 m 2 - K / k W for this run, and hence the change in (1/U) was 95% given a final Rf of 0.3 m 2 - K / k W . Sample Calculations 126 D .6 Calculation of parameters presented in Table 6.1 — - — E (Ttop^  + Tmid^  + Tbot^\ (D.13) ^ t=s.s. ^ ^ Ttn = 1 JT Ttn(t) (D.14) t=s.s. T 6 = — E fTin^ + r°«t(*A (D.15) ^ t=5.5. V 2 y Q = ^ E (D-16) t=S.S. ™̂ = IT E a t " « W ( D - 1 7 ) " , = S . S . (D.18) where t r is the total recirculation time, N is the number of data points from S.S. to tr, and ATlm(t) is given by Equation D.5.

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