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Fouling rates from a sodium sulphate : water solution in supercritical water oxidation reactors Teshima, Paul 1997

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Fouling Rates from a Sodium Sulphate - Water Solution in Supercritical Water Oxidation Reactors By Paul Teshima B.Sc. (Eng. Physics) Queen's University, 1995 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE STUDIES DEPARTMENT OF MECHANICAL ENGINEERING We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA October, 1997 © Paul Teshima, 1997 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 The University of British Columbia Vancouver, Canada Date \ W \ZJn DE-6 (2/88) Abstract Supercritical water oxidation (SCWO) is a process for destruction of hazardous organic compounds in aqueous waste streams, and does not produce the environmental and/or publicity problems produced by the air emissions of waste incinerators. The process dissolves organics and an oxidizer into high pressure (25 MPa) and high temperature (300 - 400 °C) water. In a reactor, the temperature is increased (above 400 °C) and the hazardous compounds oxidize, and are converted to carbon dioxide, ash and water. Supercritical water oxidation has been proposed as a treatment technique for pulp sludges, United States Department of Energy special wastes, metabolic byproducts and specialized chemical waste streams. A number of practical difficulties prevent widespread commercialization of SCWO. An important problem is that salts dissolved in the waste streams become insoluble at supercritical conditions and precipitate out of solution in the reactor. These salts then deposit on the reactor tube wall leading to a flow restriction. The fundamental aspects of salt deposition are not understood. The solubility of common salts in supercritical water is not well documented, and the factors that influence deposition rates are not known. In order to design SCWO systems to handle fouling from salts, both solubility and deposition studies must be investigated. A computer program was written to aid in examining the deposition mechanisms of fouling from sodium sulphate, and their influences on friction and heat transfer. The program assumed fully developed flow in a horizontal tube, in which buoyancy was neglected, with Reynolds numbers in the range of 33000 - 180000. Four salt deposition models were incorporated into the computer program which examined the deposition rates from molecular diffusion compared to particle fouling. In each of the deposition models, it was assumed that there was no surface resistance to the attachment of salt molecules and/or particles. In one of the models, it was assumed that particles would nucleate and grow rapidly to a diameter of 2 urn. Another of the models assumed that nucleation was inhibited. A SCWO facility with a design water flow of 1 kg/min was constructed to study the salt deposition problem. Initial experiments discovered that solubilities of sodium ii sulphate at 25 MPa, and 380 to 500 °C appeared to match higher and lower temperature measurements by other researchers. Within the temperature error (± 1°C) of the solubility measurements, a rapid decrease in the solubility occurred at the pseudo-critical temperature (385.0 °C at 25 MPa). In the present work, salt deposition studies used outside surface temperatures of a fouled, heated tube as a method of inferring salt thickness profiles. Model predictions of fouling rates were reasonably close to the measurements. Predicted and measured peak salt layer heights were within a factor of two, but the location was not accurately predicted. The model predictions were most sensitive to the temperature error in the solubility equation derived from the experiments and the estimation of the properties of sodium sulphate used in calculation of the mass transfer coefficient. Additionally it was discovered that particle deposition was not important for the experimental conditions of this study, as the molecular diffusion rate kept the salt solution below saturation as it was heated. Comparing measured pressure drops with friction calculations, it was apparent that the salt deposit roughness was much less than the thickness itself. iii Table of Contents A B S T R A C T . . . ii T A B L E O F C O N T E N T S iv LIST O F F I G U R E S viii LIST O F T A B L E S xii LIST O F S Y M B O L S xi" A C K N O W L E D G E M E N T xviii 1. I N T R O D U C T I O N 1 1.1 SUPERCRITICAL W A T E R 1 1.2 SUPERCRITICAL W A T E R OXIDATION REACTORS 2 1.3 SCOPE A N D OUTLINE OF THESIS 4 2. L I T E R A T U R E R E V I E W 6 2.1 OVERVIEW 6 2.2 SCWO R E A C T O R DESIGNS 6 2.2.1 M O D A R Reactor 7 2.2.2 M O D E C Reactor 8 2.2.3 Transpiring-Wall SCWO Reactor 9 2.3 POTENTIAL C O M M E R C I A L APPLICATION OF SCWO 12 2.3.1 Huntsman's Commercial Plant 15 2.4 H E A T TRANSFER CORRELATIONS FOR SUPERCRITICAL W A T E R 16 2.5 SALT DEPOSITION R E S E A R C H 19 2.5.1 Phase Equilibria of Sodium Sulphate and Sodium Chloride 20 2.5.2 Kinetics of Salt Nucleation and Deposition 25 2.5.2.7 Salt Nucleation Studies 25 2.5.2.2 Deposition Rates from a Sodium Sulphate Solution 27 iv 2.5.2.3 A Simple Salt Deposition Model. 29 3. COMPUTER MODEL OF HEAT TRANSFER AND SALT DEPOSITION 31 3.1 OVERVIEW 31 3.2 HEAT TRANSFER PROGRAM 32 3.2.1 Thermodynamic and Transport Properties of Water. 32 3.2.2 Energy Balance 32 3.2.3 Predicting the Inside Wall Temperature 34 3.2.4 Predicting the Outside Wall Temperature..... 34 3.3 SALT DEPOSITION PROGRAM 37 3.3.1 Molecular Diffusion Rates 37 3.3.2 Model 1: Suspended Particles 44 3.3.3 Model 2: No Nucleation 46 3.3.4 Model 3: Chan et al. (1994) 46 3.3.5 Model 4: Complete..... 49 3.3.6 Salt Layer Growth Rate 53 3.3.7 Model Implementation 55 3.4 PRELIMINARY CONCLUSIONS FROM THE PROGRAM 55 4. EXPERIMENTAL APPARATUS 58 4.1 THE SCWO SYSTEM 58 4.2 INSTRUMENTATION 63 4.2.1 Temperature Measurements 63 4.2.2 Pressure Measurements 65 4.2.3 Power Measurements 66 4.2.4 Fluid Conductivity Measurements 67 4.3 DATA ACQUISITION 69 5. EXPERIMENTAL PROCEDURE AND ANALYSIS 71 5.1 OPERATION OF THE SCWO SYSTEM 71 5.2 PURE WATER HEAT TRANSFER MEASUREMENTS 72 v 5.2.1 Heat Losses in the Test Section 72 5.2.2 Testing the Thermocouple Measurement Accuracy 74 5.3 SODIUM SULPHATE SOLUBILITY EXPERIMENTS 76 5.3.1 Procedure 76 5.3.2 Producing the Solubility Curve 79 5.3.3 Analysis and Comparison of Solubility Data 79 5.3.4 Curve Fitting the Sodium Sulphate in Water Solubility Limit 81 5.3.5 Evaluating the Error of the Solubility Data 82 5.4 SODIUM SULPHATE DEPOSITION EXPERIMENTS 85 5.4.1 Procedure 85 5.4.2 Mass Balance 86 5.4.3 Inferences from Temperature Measurement 89 5.4.4 Program Procedures for Comparing Predictions to Experimental Data 91 5.4.4.1 Predicting the Outside Wall Temperature for a Fouled Tube 92 5.4.4.2 Estimation of Increased Flow Resistance 97 5.5 COMPARING THE EXPERIMENTAL SALT DEPOSITION PROFILES WITH THE MODEL PREDICTIONS 98 5.5.1 Modelling the Salt Deposition in the Second Preheater 100 5.5.2 Supersaturation in the Test Section 104 5.5.3 Salt Layer Location, Peak Thickness, and Shape 104 5.5 4 The Effect of a ± 1 °C Error in the Solubility Curve on the Model Predictions for Salt Deposition 110 5.5.5 Comparison Between the Model-Predicted and Experimentally Measured Pressure Drop Along the Fouled Test Section 112 6. CONCLUSIONS 115 7. RECOMMENDATIONS 117 REFERENCES 119 vi APPENDIX A: THERMOCOUPLE POSITION ON THE HEATED AREA OF THE TEST SECTION 124 APPENDIX B: COMPARISON OF THE MODEL-PREDICTED AND EXPERIMENTAL SALT DEPOSITION PROFILES 125 APPENDK C: COMPARISON OF THE MODEL-PREDICTED AND EXPERIMENTAL SALT DEPOSITION PROFILES FOR A MODOTED MASS TRANSFER COEFFICIENT 133 APPENDK D: DATA FILES FOR THE EXPERIMENTAL RUNS AND RESULTS 141 APPENDIX E: BUOYANCY CALCULATIONS 142 APPENDK F: SOURCE CODE FOR THE COMPUTER PROGRAMS SCHEAT.F AND SALT.F 143 COMPUTER PROGRAM SCHEAT.F .144 SAMPLE INPUT FOR SCHEAT.F 154 SAMPLE OUTPUT FILE FROM SCHEAT.F 155 COMPUTER PROGRAM SALT.F 156 SAMPLE INPUT FOR SALT.F 161 SAMPLE OUTPUT FILE FROM SALT.F 162 FUNCTIONS FOR SCHEAT.F AND SALT.F 163 vii List of Figures Chapter 1 Figure 1.1: The temperature, pressure phase diagram for water 1 Figure 1.2: Schematic of the SCWO process 3 Chapter 2 Figure 2.1: MODAR vessel reactor. Adapted from Barrier et al. (1992) 8 Figure 2.2: MODEC reactor for SCWO treatment. Adapted from Modell (1990) 9 Figure 2.3: Transpiring-wall SCWO reactor 10 Figure 2.4: Summary of previous data on the solubility of sodium sulphate in water. Chan et al.'s (1994) data was taken at 27 MPa and Morey and Hesselgesser's (1951) data point was interpolated between pressures of 13.3 and 66.6 MPa. All other data points are for 25 MPa ..21 Figure 2.5: Phase diagram for the system of sodium chloride and water at 25 MPa 24 Figure 2.6: Schematic of cell interior during the flow/shock crystallization experiments. Adapted from Armellini and Tester (1991) 26 Figure 2.7: Schematic of the 1.91 cm (inner diameter) Swagelok cross used for the deposition experiments on the heated cylinder ('hot finger'). Sapphire windows can be placed in any of the shaded ports. Flow is in and out of the page. Adapted from Hodesetal. (1997) 28 Chapter 3 Figure 3.1: The step-wise method of the heat transfer program SCHeat.f. 33 Figure 3.2: Flowchart describing the iterative procedure used in calculating the inside wall temperature with an initial Nusselt number estimate with only bulk properties.. 35 Figure 3.3: Schematic diagram of the salt deposition mechanisms occurring in one length-step for Model 1: Suspended Particles r.... 45 Figure 3.4: Schematic diagram of the salt deposition mechanisms occurring in one length-step for Model 2: No Nucleation 47 viii Figure 3.5: Schematic diagram of salt deposition mechanism occurring in one length-step for Model 3: Chan et al. (1994) 48 Figure 3.6: Schematic diagram of salt deposition mechanisms occurring in one length-step for Model 4: Complete 50 Figure 3.7: Outline of time-step implementation in the program for correction of decreasing tube diameter and deposition surface area 56 Chapter 4 Figure 4.1: The UBC / NORAM SCWO facility 59 Figure 4.2: Electrical heating schematic for the preheaters and test section 61 Figure 4.3: The test section of the SCWO system 61 Figure 4.4: Position of the bulk and surface thermocouples on the test section 63 Figure 4.5: Spot welded attachment of surface thermocouples 64 Figure 4.6: Differential (DP) and absolute (P) pressure cells in the test section 65 Figure 4.7: Installation of the conductivity meter probe 67 Figure 4.8: Calibration of the Conductivity Meter 68 Figure 4.9: Data Acquisition System for the SCWO Facility 70 Chapter 5 Figure 5.1: Comparison of experimental and model temperature profiles for distilled water in a heated test section at 25 MPa and sub-critical temperatures 75 Figure 5.2: Comparison of experimental and model generated temperature profiles in a heated test section at 25 MPa and near critical temperatures 75 Figure 5.3: Experimental method for salt solubility experiments 77 Figure 5.4: Summary of data for solubility of sodium sulphate in water at 25 MPa 80 Figure 5.5: Curve fit to the solubility data for sodium sulphate in water at 25 MPa 83 Figure 5.6: Comparison of similar runs, to determine the reproducibility of the experiments 90 Figure 5.7: The algorithm for the program Salt.f which converts the outside surface temperature data to a salt layer thickness 94 ix Figure 5.8: Calculation of the salt layer volume by approximating the layer as a series of 'cylinders'of length Az and wall thickness ys lJt 95 Figure 5.9: Algorithm used to determine the thermal conductivity of sodium sulphate.. 96 Figure 5.10: Comparison of experimental and predicted salt deposition profiles for sodium sulphate in a heated tube at 25 MPa and near critical temperatures 99 Figure 5.11: Saturation of the solution along the test section for salt deposition experiments with Na2S0 4 at 25 MPa and sub- to supercritical temperatures 105 Figure 5.12: Model predictions for run 14, extended by another test section length to compare the molecular and particle deposition rates 106 Figure 5.13: Model predictions for run 14, extended by two test section lengths to compare the molecular and particle deposition rates 106 Figure 5.14: Comparison of the height and location of the peak of the salt layer 108 Figure 5.15: Comparison of the height and location of the peak of the salt layer 108 Figure 5.16: Effect of a ± 1 0 C temperature error in the solubility curve on the model predictions Ill Figure 5.17: Comparison between the model predicted and the experimentally measured pressure drop along the fouled test section 113 Appendix B Figure B l : Comparison between model and experimental data for run 1 ...126 Figure B2: Comparison between model and experimental data for run 2 126 Figure B3: Comparison between model and experimental data for run 3 127 Figure B4: Comparison between model and experimental data for run 4 127 Figure B5: Comparison between model and experimental data for run 5 128 Figure B6: Comparison between model and experimental data for run 9 128 Figure B7: Comparison between model and experimental data for run 10 129 Figure B8: Comparison between model and experimental data for run 11 129 Figure B9: Comparison between model and experimental data for run 12 130 Figure B10: Comparison between model and experimental data for runl3 130 Figure B l l : Comparison between model and experimental data for run 14 131 x Figure B12: Run 1 model predictions corrected for preheater fouling 132 Figure B13: Run 2 model predictions corrected for preheater fouling 132 Appendix C Figure CI: Comparison between model and experimental data for run 1 134 Figure C2: Comparison between model and experimental data for run 2 134 Figure C3: Comparison between model and experimental data for run 3 135 Figure C4: Comparison between model and experimental data for run 4 135 Figure C5: Comparison between model and experimental data for run 5 136 Figure C6: Comparison between model and experimental data for run 9 136 Figure C7: Comparison between model and experimental data for run 10 137 Figure C8: Comparison between model and experimental data for run 11 137 Figure C9: Comparison between model and experimental data for run 12 138 Figure CIO: Comparison between model and experimental data for run 13 138 Figure C l l : Comparison between model and experimental data for run 14 139 Figure C12: Run 1 model predictions corrected for preheater fouling 140 Figure C13: Run 2 model predictions corrected for preheater fouling 140 xi List of Tables Chapter 2 Table 2.1: Overall reactions in supercritical water oxidation 14 Table 2.2: Destruction efficiencies of hazardous organics by SCWO 14 Table 2.3: Comparison between model and experimental data (Chan et al., 1994) 29 Chapter 5 Table 5.1: Results of heat loss experiments 73 Table 5.2: Results for extrapolation of low mass flow, heat loss data to the high mass flow condition 74 Table 5.3: Salt deposition effluent concentrations used as an error estimate on the solubility experiments 84 Table 5.4: Salt deposition experiments summary 86 Table 5.5: The results of the mass balance for the last six salt deposition runs. A comparison between the salt delivered to the system and the salt collected at the outlet 87 Table 5.6: Summary of equal mass delivery calculations 90 Table 5.7: Comparison between model predictions and experimental data 99 Table 5.8: Model predictions investigating the possibility of salt deposition to the hot tube wall in the second preheater 103 Table 5.9: Comparison between model predictions and experimental data of the peak heights and location of the salt layer 107 Appendix A Table A l : Thermocouple position on the heated area of test section 124 Table D1: Summary of data files 142 xii List of Symbols A = ratio of r; / r a = constant in Nusselt number correlation [-] B = constant in free convective Nusselt number calculation [-] b = constant in Nusselt number correlation [-] bk = Boltzman's constant [J/K] C = concentration of salt solution [wt%] C A = concentration of species A [wt%] cb = concentration of dissolved salt in the bulk fluid [wt%] Cbp = concentration of particles in bulk fluid [wt%] Cbpw = concentration of particles at the wall (= 0 ) [wt%] Cmol = concentration of molecules diffusing to the wall [wt%] Csat = concentration of the solubility limit [wt%] Cw = concentration of dissolved salt at the wall [wt%] c = constant in Nusselt number correlation H = specific heat capacity of the fluid [kJ/kg-K] = integrated specific heat capacity of the fluid [kJ/kg-K] D = diffusion coefficient [m2/s] d = diameter of the tube [m] dfoui = diameter of fluid flow in fouled section of tube [m] dm = molecular diameter of the salt [m] dp = particle diameter of the salt [m] dT = exact differential unit of temperature [K] f = friction factor [-] G = mass flux of fluid [kg/s-m2] g = gravitational acceleration constant [m/s2] Grf = Grashof number evaluated at the film temperature [-] H, = specific enthalpy of the fluid at the start of each length-step [kJ/kg] xiii H 2 = specific enthalpy of the fluid at the end of each length-step [kJ/kg] Hb = specific enthalpy of the bulk fluid [kJ/kg] Hi„ = specific enthalpy of the inlet bulk fluid [kJ/kg] HinPH2 = specific enthalpy of the inlet bulk fluid of the second preheater [kJ/kg] HjnTS = specific enthalpy of the inlet bulk fluid of the test section [kJ/kg] Hout = specific enthalpy of the outlet bulk fluid [kJ/kg] HoutPH2 = specific enthalpy of the outlet bulk fluid of the second preheater [kJ/kg] H w = specific enthalpy of the fluid at the inside wall temperature [kJ/kg] h = heat transfer coefficient [kW/m2-1 = mass transfer coefficient [m/s] k = thermal conductivity of the fluid [W/m-K] kb = thermal conductivity of the bulk fluid [W/m-K] kf = thermal conductivity of the fluid at the film temperature [W/m-K] klayer = thermal conductivity of the salt layer [W/m-K] k,alt = thermal conductivity of the salt [W/m-K] ktube = thermal conductivity of the tube [W/m-K] kw = thermal conductivity of the fluid at the inside wall temperature [W/m-K] Le = Lewis number H Le„ = Lewis number evaluated with wall properties [-] rh = mass flow of the fluid [kg/s] mmol = molecular diffusion rate of salt [kg/s] mpart = particle deposition rate [kg/s] msalt = overall salt deposition rate [kg/s] m water = mass flow of water [kg/s] TWlect = mass of salt collected in sample jugs [kg] rriexp = mass of salt layer calculated from the mass balance [kg] nifiuid = mass of the fluid [kg] miayer = mass of salt layer calculated by the models [kg] = mass of salt [kg] xiv N = number of molecules of the salt in 1 cm3 [-] n = constant in free convective Nusselt number calculation [-] Nu = Nusselt number [-] Nm = Nusselt number used in wall temperature iterations [-] Nu2 = Nusselt number used in wall temperature iterations H Nuf = Nusselt number evaluated with film temperature properties H P = the absolute pressure of the system [MPa] Pr = Prandtl number [-] PTf = Prandtl number evaluated with film temperature properties [-] Qloss = total heat loss in section of system [kW] Qtotal = total heat applied in section of system [kW] q = heat flux per unit length [kW/m] q2 = heat flux per unit area [kW/m2] r = radial distance from centre of the tube [m] r; = inside radius of the tube [m] r„ = radial distance from the centre of the tube to the salt layer [m] Re = Reynolds number [-] Ref = Reynolds number evaluated with film temperature properties [-] Sc = Schmidt number [-] Sh = Sherwood number [-] T b = bulk temperature of the fluid [K] T e = outside wall temperature of the tube [K] T f = film temperature [K] T 8 = temperature of surface of salt layer in contact with fluid [K] T w = inside wall temperature of the tube [K] Twi = inside wall temperature used in wall temperature iterations [K] T W2 = inside wall temperature used in wall temperature iterations [K] T „ = ambient temperature of surrounding fluid [K] t = total fouling time [s] tp = time until salt layer completely 'plugs' the tube [min] XV u = mean velocity of the bulk fluid in the z-direction [m/s] * u = wall friction velocity of fluid [m/s] V = volume [m3] V S = total volume of salt in the salt layer [m3] V T = total volume of the salt layer [m3] v d = particle deposition velocity [m/s] = dimensionless particle deposition velocity [-] V O U T = voltage output from differential pressure transducers [V] VRMS = root mean square voltage applied to the tube [RMS V] V = mean velocity of the bulk fluid in the y-direction [m/s] Yexp = experimental salt layer thickness [mm] Ymodel = model-predicted salt layer thickness [mm] Ysalt = thickness of salt layer [mm] Z = length of tube [m] Zexp = experimental axial location of peak of salt layer [m] Zmodel = model-predicted axial location of peak of salt layer [m] Greek Symbols AP = differential pressure [kPa] Am = percentage difference for mass balance [%] At = length of one time-step in the program [s] Az = length of the axial step-size used by the program [m] a = thermal diffusivity [m2/s] Pf = volumetric expansion coefficient at film temperature [1/K] E = tube roughness [mm] Bfoul = roughness of a fouled tube [mm] • = porosity of salt layer [-] = dynamic viscosity of the fluid [kg/s-m] = dynamic viscosity of the fluid at the film temperature [kg/s-m] xvi Uw = dynamic viscosity of the fluid at the inside wall temperature [kg/s-m] p = density of the fluid [kg/m3] Pb = density of the bulk fluid [kg/m3] Pf = density of the fluid at film temperature [kg/m3] Pent = density of the fluid near the critical region [kg/m3] Player = density of the salt layer [kg/m3] Psait = density of the salt [kg/m3] Pw = density of the fluid at the inside wall temperature [kg/m3] a = electrical conductivity of the salt solution [u,S/cm] TP = particle relaxation time [s] T P + = dimensionless particle relaxation time [-] xw = wall shear stress [N/m2] xvii Acknowledgment First and foremost I thank Dr. Steven Rogak, my supervisor, whose insight and support was never ending. Through his help and guidance, I achieved more, at a higher level of understanding than I had hoped. I thank Dr. Dan Fraser who also provided much of the needed drive and helpful criticisms necessary to complete this work. Dr. Hill and Dr. Branion were also extremely helpful with their comments and attention to the project. I thank my colleagues. Mike Savage, Alex Podut, Tazim Rehmat, Majid Bazargan, Danijela Filipovic, Madalina Arama and Chris Kirby, whose constant involvement were integral for the success of this project. The personnel at NORAM Engineering & Constructors Ltd. must also be acknowledged for their engineering skills and dedication. In particular, I thank John Lota, Stuart Gairns and Ed Hauptmann for both their professional and personal support. Many others were also involved with the construction of the facility I thank Sean Bygrave, who found everything I needed on time, and the mechanical shop personnel: Anton Schreinders, Doug Yuen, Len Drakes, Benny Nimmervoll, and John Richards, for without their expertise we would still be bolting together dexion. Finally I thank my parents and friends, who kept me going and kept me smiling. xviii 1. Introduction 1.1 Supercritical Water The critical point of water is 647 K and 221 atm (figure 1.1). Above this temperature and pressure water becomes supercritical and exists in only one phase as a fluid (Van Wylen et al., 1994). Supercritical water has many properties that differ from water at ambient conditions. The density of water changes rapidly with both temperature and pressure around the critical point. At the critical temperature, water can change from "liquid-like" to "gas-like" over the pressure range of a few hundred bar (Shaw et al., 1991). Figure 1.1: The temperature, pressure phase diagram for water For the conditions typical of this study, supercritical water has a density of water of about 0.1 g/cm3, compared to the normal water density of about 1 g/cm3. Supercritical water also has high self-diffusion coefficients and low viscosity. Solute molecules can 1 diffuse more readily through the supercritical water than water at ambient conditions creating a more reactive medium (Shaw et al., 1991). An important property of supercritical water is its ability to dissolve the organic compounds that are insoluble in ambient water. This is related to the variation of the dielectric constant at supercritical conditions. At 250 atm. the dielectric constant ranges from 80 at 25 °C to 2 at 450 °C (Tester et al., 1991). At 25 °C water effectively shields the charge of ions, enabling ionic compounds (e.g. sodium sulphate) to dissolve. At supercritical temperatures, the electrostatic potential between ions is poorly shielded, and supercritical water acts like a non-polar dense gas enabling it to dissolve non-polar organic compounds (Shaw et al., 1991). However, the low dielectric constant at supercritical conditions also reduces the solubility of ionic compounds (salts). 1.2 Supercritical Water Oxidation Reactors SCWO is a process which utilizes supercritical water as a medium for the destruction of organic materials. Supercritical water, organics and oxygen are mixed together at high temperatures and pressures. Under these conditions a single phase fluid reaction system exists and allows for intimate molecular contact. With no inter-phase transport limitations, oxidation is relatively rapid (Tester et al., 1991). In figure 1.2 a simplified SCWO facility is depicted. Water, wastes and the oxidizer (often oxygen) are pressurized to 25 MPa. In the pre-heater (or regenerative heat exchanger) this multiphase mixture is heated past the critical temperature (647K) where the organics and oxidizer dissolve in the water. At this temperature the oxidation reaction begins and the rate of oxidation increases rapidly as the temperature is increased. The waste stream then proceeds into an insulated reactor and continues to oxidize, releasing heat. The mixture is then cooled in a heat exchanger and de-pressurized. The effluent is separated into CO2 , water and a small amount of solids (ash). 2 Oxygen Water & Organics Heating Single Phase Reaction Cooling Separation CO, Water Ash Figure 1.2: Schematic of the SCWO process. Over the past decade supercritical water oxidation has undergone much development. But due to several significant issues related to the process, SCWO has not become fully commercialized. Two of the main problems are related to heat transfer and fouling due to salt deposition. In a supercritical water oxidation facility, the design of the reactor and the heat exchangers directly affects the efficiency of the process. For commercialization it is important that these components are optimized for performance. The thermodynamic and transport properties of fluids vary dramatically in the critical region. These variations can make it difficult to model the heat transfer in and around the critical point. Heat transfer coefficients for the critical region are needed for optimum design of an SCWO system. The second problem involves fouling by salt deposits. While subcritical water is a good solvent for salts, supercritical water is a poor solvent for salts. Salt deposition affects the heat transfer in the system and the pressure drop in the reactor. Salts can originate from several different sources. They can be present in the waste stream and precipitate out of solution at reaction conditions. In a tubular reactor, these salts deposit on the reactor wall and eventually interfere with the processing of organic components by causing a flow restriction in the reactor leading to an increase in pressure. Complete plugging of a SCWO reactor can happen in less than an hour (if the salt concentrations are 3 high), and requires the facility to be shut down for cleaning. The mechanisms affecting salt deposition must be studied to provide proper prevention techniques for a SCWO system. 1.3 Scope and Outline of Thesis In 1996, a joint project involving UBC, NORAM Engineering & Constructors Ltd., and the Science Council of British Columbia was initiated to build a SCWO pilot plant and obtain engineering and fundamental data on heat transfer and fouling. The present study examines the fouling process of Na2S04 (sodium sulphate) in a tubular supercritical water oxidation reactor. To understand the complex nature of the fouling problem in SCWO, the development of the process and reactor design are discussed in chapter 2. Important work completed with salts in supercritical water is examined, mainly focusing on the solubility of sodium sulphate in water and a simple deposition model for a salt solution flowing in a heated tube near critical conditions. A heat transfer / salt deposition computer program was written to aid in the design of the SCWO facility and experiments. The structure, equations and assumptions made in the program are explained in chapter 3. Some preliminary modelling of the system was completed to estimate fouling times and magnitudes of experimental measurements and is also included in chapter 3. The SCWO facility was then constructed for the salt deposition experiments. With the aid of the computer program, an experimental section (test section) was designed to obtain temperature and pressure measurements of the process fluid. The main components of the facility (for both process and safety issues) and test section instrumentation are described in chapter 4. Using temperature ranges and salt solution concentrations based on previous work contained in chapter 2 and modelling results in chapter 3, solubility and salt deposition experiments were performed using the SCWO system. Sodium sulphate was chosen due 4 to the fact that similar work has been completed by Chan et al. at Sandia (1994). In chapter 5 the procedure used in the experiments is outlined and the results are compared to the modelling predictions. Finally the conclusions from the salt deposition studies are discussed in chapter 6. The conclusions focus on the comparison between molecular and particle deposition rates and the factors that this study indicates are most influential in the fouling process. The recommendations for future work that are contained in chapter 7. 5 2. Literature Review 2.1 Overview Both heat transfer and salt deposition issues are critical for SCWO system design, and there are many types of SCWO reactors which handle these problems differently. Three designs of SCWO reactors are explained, each with advantages and disadvantages over the others. Reactor designs must also consider the type of wastes that would be processed, to achieve adequate residence times for the required destruction efficiencies. The types of wastes targeted for disposal with SCWO are discussed, including a description of the only commercial plant in Austin, Texas. With only one commercial facility, it is obvious that the problems with SCWO are still prevalent. One problem is that modelling the heat transfer to supercritical water is difficult. To model the critical region, many heat transfer correlations have been formulated and are discussed. Another problem associated with SCWO is fouling from precipitated salts in supercritical water. Solubility of salts in supercritical water is not well documented. Previous phase equilibria experiments with sodium chloride and sodium sulphate solutions (with water) are reviewed. Broad overviews of SCWO technology and research are given by Tester et al. (1991), Gloyna and L i (1995), and Shaw et al. (1991). 2.2 SCWO Reactor Designs There are several different reactor designs which handle the problems of heat transfer and salt deposition differently. To begin with there are two distinct categories of SCWO systems. The first is an above ground system which uses high pressure pumps and compressors to achieve system pressure. The second is a below ground system or deep well reactor, which uses the hydraulic head of the fluid in a well to create the high pressures needed for the process. Calculations performed by Stanford and Gloyna (1991) with the second method (deep well) suggests that the energy saved by not using a high pressure pump is offset by the heat losses to the surrounding rock and energy needed 6 during start up of the reactor. For these reasons, more work has been concentrated on the above ground system. In particular, three types of reactor designs have been implemented, the MODAR or vessel reactor (Hong et al., 1989), the MODEC or tubular reactor (Modell, 1990), and the Transpiring-Wall SCWO Reactor (McGuinness, 1995). 2.2.1 MODAR Reactor The MODAR type reactor (Bamer et al., 1992; Hong et al., 1989; Bettinger and Killilea, 1995) uses a vertical cylindrical vessel which is composed of two temperature zones. The first is a supercritical region in which the pressurized waste stream and oxidant are injected through a coaxial nozzle into the hot zone of the vessel, located at the top (see figure 2.1). As the oxidation reaction occurs, gaseous effluents in this phase are discharged through the effluent line at the top of the vessel. Any salts that precipitate out of solution will fall to the bottom of the reactor where a cooler zone of water will re-dissolve the particulate salts. The cooler zone is kept at a lower temperature through the injection of cold water. The brine solution is then directed out of the bottom of the reactor for analysis or disposal. With the vessel reactor, there are some key design issues. To begin with, due to the large diameter of the vessel and high pressures of the system, the reactor must be made from a high strength nickel alloy with extremely thick walls which is costly. Additionally, the two essential components of the process inside the reactor are the proper mixing of the waste, oxidizer and supercritical water in the hot zone, and the control of precipitated salts in the cold zone. Part of the difficulty in achieving these two design criteria is the large temperature and density gradients axially in the reactor due to the two temperature zones (Barner et al., 1992). Another problem is the deposition of the sticky salts on the sides of the reactor as they fall into the cold zone to be re-dissolved. The majority of salts precipitating out of the waste stream are directed (by the jet stream) or fall into the cooler zone of the reactor where they will re-dissolve and be removed in solution. The velocity profile of the vessel reactor does have some radial components, which will allow some of the sticky salts to move to the wall where they adhere and accumulate. 7 Air and Water J Waste and Caustic Hot Zone { t Effluent Cold Watei/ Y Cooler Zone 1 Brine Figure 2.1: MODAR vessel reactor. Adapted from Barrier et al. (1992). 2.2.2 M O D E C Reactor The MODEC (Modell, 1990) tubular (figure 2.2), or plug-flow reactor uses a long small diameter tube (e.g. 0.95 cm. O.D.,0.63cm. I.D. for pilot plant at UBC) to contain the oxidation reaction as it proceeds to completion. The wastes, oxidizer and water are premixed before the reactor, unlike in the MODAR reactor, so that complete mixing at reaction conditions is not an important process variable. With the plug-flow design, all of the process fluid will pass through the same temperature regions in the reactor, assuring reproducible oxidation results. Also due to the small diameter tubing used, standard tubing sizes can be used to contain system pressure (unlike the vessel reactor). The 8 Preheater Insulated Reactor Cooler Flow Pump External Heat Transfer Loop Figure 2.2: MODEC reactor for SCWO treatment. Adaptedfrom Modell (1990). disadvantage of the small tubing is the detrimental effect that fouling from salt particulates has on the systems ability for continuous operation. 2.2.3 Transpiring-Wall SCWO Reactor This reactor design (figure 2.3) uses a MODAR type vessel reactor for the oxidation reaction, but has an interesting method for salt deposition prevention. The key feature to this reactor is that the supercritical regions are enclosed within a permeable (transpiring) wall (13) (McGuinness, 1995; Ahluwalia et al., 1995). Supercritical water and an oxidizer are injected into the reactor at the two inlet ports (1 and 5b). Waste is introduced into the reactor through another inlet port (5a). In the pre-combustion chamber the water and oxidizer (from port 5b), and waste are completely mixed and ignited. This creates a turbulent diffusion-type reaction zone. The flow from the pre-combustion chamber enters the reaction zone (4) which is designed to achieve a residence time suitable for standard destruction efficiencies (99.9 - 99.9999% depending on waste type). The water and oxidizer jet entering at port (1) flow into the annulus created by the vessel wall and the transpiring liner. The flow pattern created is radially inward, which 9 Waste Inlet (5a) Vapour Outlet Brine & Solids Outlet (12) Figure 2.3: Transpiring--wa.il SCWO reactor 10 provides cooling to the liner and flushes particles away from the wall. It also dilutes any corrosive solutions near the wall, and provides an additional oxidizer for unreacted waste. After the reaction zone (4), the process fluid enters a transpiring-wall quench cooler (8). The cooler uses liquid brine which is re-circulated from the brine separator (9). The effluent then enters the vapour/liquid separator (9), which separates the vapour (11) from the liquid/solid particulate fluids (12). There are many advantages with this type of system. There is the immediate resistance to salt deposition of the walls of the vessel due to the injected supercritical water stream into the annulus (2). This same effect reduces corrosion (see section 2.3) at the inner walls, which increases the durability and strength of reactor. The re-circulating brine solution (6) as part of the quench cooler can be altered with different chemicals to control the effluent composition, therefore controlling the emissions of the reactor. Finally the closed-cycle system efficiently recycles and reuses process fluid; using water for influent recovered from the hot vapour steam leaving the brine separator, and using cold brine from the brine separator in the quench cooler. Some of the disadvantages are that this type of reactor design is costly due to the large diameter vessel. If any salt deposition does occur, it would be difficult to clean without disassembly. Also as with the MODAR type reactor, the complete mixing of the reactants in the hot reaction zone is important, and must be controlled for high destruction efficiencies. It is important to note that the only SCWO commercial facility operating at the present is the Huntsman Plant in Austin, Texas (McBrayer and Griffith, 1996) and uses a tubular reactor design. However, the Huntsman plant requires downtime every two weeks to clean fouled sections and can only process specific wastes (see section 2.3,1). This indicates that the fouling problem has not yet been resolved with reactor design and is affected directly by waste type. Therefore the design issues cannot be addressed without understanding what wastes the SCWO process may be used for in a commercial application. 11 2.3 Potential Commercial Application of SCWO In this section, we consider applications where SCWO might be used to advantage. Generally, these are for wet wastes that can be pumped. One of the first waste types that SCWO was considered for was for pulp mill sludges. Historically, waste treatment sludges were thought of as benign, with land filling being the most appropriate method of disposal (Blosser and Miner, 1986). For a pulp mill, the land filling cost for pulp mill sludge was very small in compared to the overall operations cost. More recently, dioxins were discovered in waste treatment sludges and effluents. This created some concern with the U.S. Environmental Protection Agency (EPA) in the prevalent method of disposal (U.S. EPA, 1988). Although dioxin formation can be reduced significantly by substituting chlorine dioxide instead of chlorine as the bleaching chemical (Modell et al., 1991), there are many other chemicals of concern in waste water treatment sludges (e.g. chlorination of sewage treatment plant effluent creates chlorinated hydrocarbons (U.S. EPA, 1982)). It became apparent that land disposal of pulp mill sludges was creating many problems and an alternative needed to be substituted. Two effective methods used for processing dilute wastes (< lwt% organics) are activated carbon absorption, and biological oxidation. For activated carbon absorption, the major cost in the process is in regenerating the carbon. The carbon loading is directly proportional to the organic concentration, and therefore the process becomes more and more expensive if the concentration of the waste exceeds 1 wt%. The problem with biological oxidation processes is that they cannot be sustained when the organic concentration in the wastes exceed a few wt% (Tester et al., 1991). Additionally these methods may remove contaminants from a waste stream but do not necessarily destroy the compound. Another alternative disposal method is incineration. In order to achieve the high destruction efficiencies required for the hazardous and toxic wastes, temperatures during the process must be very high (900 - 1300 °C). In the case of aqueous wastes, the additional energy needed to vapourize the mixture is also required. This high energy process can generally sustain itself when waste streams contain more than 25 wt% 12 organics. Waste streams with an organic content less than 25% need the addition of supplemental fuel to maintain the temperatures needed for the incineration process. With decreasing organic waste concentration, incineration becomes more and more costly. Additionally with new regulations on stack emissions, expensive equipment must also be installed to remove NOx (nitric oxides), acid gases and particulates before released (Tester etal., 1991). For the range of 1 - 20 wt% organics, in waste treatment sludges, there appears to be a deficiency in an economically and environmentally acceptable disposal process. Supercritical water oxidation appears to have the ability to satisfy this area of waste treatment. At the moderate temperatures needed for the process (400 - 600 °C), a lower concentration of organics (than for incineration) is needed for the reaction to sustain itself without the addition of auxiliary fuel. Also the destruction efficiencies for SCWO are similar to incineration, typically greater than 99.99% in reduction in total organic carbon (Thomason et al., 1990). Table 2.1 (Modell et al., 1991) contains some of the overall reactions occurring in supercritical water oxidation processing. In some of the examples the products contain innocuous substances such as carbon dioxide, water and molecular nitrogen. But in the cases of processing organic chlorides and sulfides, acids are produced. Corrosion due an acidic effluent is often a problem (LaJeunesse et al., 1993), which can lead to the precipitation of salts if a base is added to neutralize the mixture. Table 2.2 (Modell et al., 1991) contains the destruction efficiencies for hazardous organics that were processed using a MODEC (tubular) SCWO system These destruction efficiencies are measured by the degree of removal of all organic matter from the feed to the effluent (except for dioxin, which is the reduction of specific feed material in the effluent). Even with the relatively short residence times ( less than 4 minutes) and moderate temperatures (less than 580 °C), the destruction efficiencies are high, ranging from 99.99% to even 99.99995% for dioxins. 13 Table 2.1: Overall reactions in supercritical water oxidation Hydrocarbons C 6H6 + 7.5 0 2 Benzene = 6C0 2 + 3H 20 Organic Chlorides Cl2-C6H2-02-C6H2-Cl2 + 11 0 2 Dioxin = 12C02 + 4HC1 Organic Sulfides C1-C2H2-S-C2H4-C1 + 7 0 2 HD = 4 C0 2 + 2 H 20 + 2 HC1 + H 2S0 4 Organic Nitrogen CH 3-C6H 2-(N0 2) 3 + 5.25 0 2 TNT = 7 C0 2 + 2.5 H 20 + 1.5 N 2 Heavy Metals Pu(N03)4 + 2 H 20 + 2 C0 2 = Pu(C03)2 + 4 HN03 Radioactive wastes Table 2.2: Destruction efficiencies of hazardous organics by SCWO CLASS/COMPOUND T Time Destruction Reference [CI [mini Efficiency T%1 Organic Nitro Compounds 2,4 - Dinitrotoluene 457 0.5 99.7 Thomason et al. (1984) 2,4 - Dinitrotoluene 513 0.5 99.992 Thomason et al. (1984) 2,4 - Dinitrotoluene 574 0.5 99.9998 Thomason et al. (1984) Halogenated Aliphatics 1,1,1 - Trichloroethane 495 3.6 99.99 Modell(1985) 1,2 - Ethylene dichloride 495 3.6 99.99 Modell (1985) 1,1,2,2 - tetrachloroethylene 495 3.6 99.99 Modell (1985) Halogenated Aromatics Hexachlorocyclopentadiene 488 3.5 99.99 Modell (1985) o-chlorotoluene 495 3.6 99.99 Modell (1985) 1,2,4 - Trichlorobenzene 495 3.6 99.99 Modell (1985) 4,4 - Dichlorobiphenyl 500 4.4 99.993 Modell (1985) DDT 505 3.7 99.997 Modell (1985) PCB 1234 510 3.7 99.99 Modell (1985) PCB 1254 510 3.7 99.99 Modell (1985) Dioxin (2,3,7,8 - TCDD) 574 3.7 99.99995 Modell (1990) SCWO has also been tested on several other waste types, such as DOE/DP surrogate wastes (Bramlette et al., 1990), secondary pulp mill sludges (Modell, 1991), and has been proposed for treatment of metabolic wastes for long term space missions (Armellini and Tester, 1990). However, the SCWO treatment of these wastes has been limited to the pilot plant level. 2.3.1 Huntsman's Commercial Plant In Austin, Texas, Huntsman Petrochemical Corporation was the first company to use SCWO commercially. Their full scale SCWO plant was designed and constructed by Eco Waste Technologies (EWT) in the spring of 1994. EWT also performed the initial plant commissioning, start-up , and verification runs on the facility. It was initially designed to run 320 days each year, 24 hours a day, though operation in the first year was limited due to plant modifications and operator training. Up to this point and time, there have been no problems related to the SCWO process, system control, and safety issues (McBrayer and Griffith, 1996). In running the plant, Huntsman has discovered that the technology is more cost efficient than off-site incineration. The facility operates at 18.5 kg/min, with a waste stream of 10 wt% organics. There is a downtime every two weeks, when the system is flushed with a nitric acid solution to remove carbonate scale deposits in the heat exchanger. The plant has successfully treated paper mill sludge, distillery sludge, non-chlorinated solvents, paint sludge, adhesives, greases, waste oils and cleaning solutions. Emission tests were carried out at steady-state operation conditions to allow permitting in California, and the results indicated low levels of priority pollutants, such as nitrogen oxides (NOx), carbon monoxide, dioxins, furans, and polychlorinated biphyenyls (McBrayer and Griffith, 1996). It appears that for a specific waste type, there are some benefits to using supercritical water oxidation. Due to the problems associated with the process (fouling effecting heat transfer and pressure drop) SCWO is not yet fully commercialized; but the growing interest in this process has lead to active research in design and modelling. Process modelling will continue to be important, in particular computer modelling of heat 15 transfer and the salt deposition problem should aid in detenriining the most effective prevention techniques when dealing with organic wastes containing salts. 2.4 Heat Transfer Correlations for Supercritical Water Conventional correlations for heat transfer to water are not valid for supercritical conditions. This is due to the fact that near the critical region the thermodynamic and transport properties of water vary dramatically. The form of the equation previously used where Nu is the Nusselt number [-] h is the heat transfer coefficient [kW/m2-K] d is the diameter of the tube [m] k is the thermal conductivity of the fluid [kW/m-K] G is the mass flux [kg/s-m2] H is the viscosity [kg/s-m] cp is the specific heat capacity of the fluid [kJ/kg-K] a, b, and c are constants [-] Many Nusselt number correlations have be determined for supercritical water in a heated tube (Yamagata et al., 1971; Mirapolsky and Shitsman, 1957; Bishop et al., 1965; Touba and McFadden, 1966; Swenson et al., 1965). All correlations used an additional term, which were various ratios of wall and bulk properties to account for the critical region (except for Mirapolsky and Shitsman). There is a fairly large discrepancy between was. (2.1) 16 predicted heat transfer coefficients (from 1.5 - 3.7 J/cm2-s-°C at the critical temperature) among the correlations (Hall, 1971), which demonstrates the difficulty in predicting the affect of the large property variation in the critical region. Reviews of heat transfer to supercritical water are given by Hall (1971) and Polyakov (1991). A correlation by Swenson et al. (1965) is consistent with many of the other correlations described in Hall (1971) and is fairly simple. Their experiments were performed using distilled, deionized water flowing through an electrically heated test section. Bulk and surface temperature thermocouples were used to determine the heat transfer coefficients. In determining their Nusselt number correlation, equation (2.1) was modified to account for the physical property variations using an integrated average specific heat taken from Petukov et al. (1961): (2.2) where cp is the integrated specific heat capacity of the fluid [kJ/kg-K] H is the specific enthalpy of the fluid [kJ/kg] Tis the temperature [K] dT is a differential unit of temperature [K] with the subscripts w and b referring to properties evaluated at the inside wall temperature and bulk temperature Th . Temperature ratios ( TJT^ ) have also been used to account for the variations across the inside film. This method was successful for gases with a regular variation of physical properties with temperature. Swenson et al. determined that density ratios ( pjph ) (inside wall to bulk) provided the best fit to experimental data. Using equations (2.1, 2.2) and the specific density ratio, Swenson et al.'s (1965) correlation was: 17 h d Nu = -—= 0.00459 U G Y 9 2 3 ( H ^ - H J ^ 0 6 1 3 ^ ^ V Av J 0.231 (2.3) where p is the density [kg/m3]. This equation can be rewritten in terms of Reynolds and Prandtl numbers: Nu =0.00459 (Re)0 9 2 3 (Pr)° 6 1 3 f \ 0.231 Av V Pb) ( 2.4) where Re is the Reynolds number and is dimensionless: pud Re = -A where u is bulk stream fluid velocity [m/s] pu = G the mass flux [kg/s-m2] The Prandtl number is also dimensionless: (2.6) To ensure the correlation was accurate for the sub-critical temperature region, several data points with film temperatures less than 371 °C (physical properties only vary moderately), were compared to the predicted values, and demonstrated very low deviation (all points lie within ± 10%). The previously (McAdams et al., 1950) accepted Nusselt number correlation for sub-critical temperatures was: 18 —— = 0.019 (2.7) where the subscript 'f' indicates evaluation at the film temperature which is an average of wall and bulk temperatures. Equation 2.7 did not compare as well to the data for near-critical temperatures. All correlations are for pure water, and the complications from the multi-component mixture encountered in SCWO systems was not considered. 2.5 Salt Deposition Research The heat transfer problem of modelling the variations in properties in supercritical water extends into the closely related area of mass transfer. The large temperature gradients that can exist from the bulk fluid to the tube wall, can make salt precipitation and deposition difficult to predict. There is very little data on the solubility of salts in supercritical water. In a review article by Tester et al. (1991), the solubility of some common salts (Na2S04, NaCl, KC1, CaCk, and CaS04) is shown to be widely varying around the critical temperature at 25 MPa. In most cases, there is a sharp decrease in solubility just above 380 °C, which then levels off past 450 °C. In the case of CaS04, the solubility actually increases again after 500 °C. When compared to the solubility at room temperature (25 °C), the concentrations are several orders of magnitude lower. A relationship between solubility and temperature is needed to predict where fouling will occur in a SCWO system. 19 2.5.1 Phase Equilibria of Sodium Sulphate and Sodium Chloride Some of the first work with the solubility of salts in superheated steam at high pressures was done by geologists. Morey and Hesselgesser (1951) measured solubility of minerals in steam up to 600 °C and 200 MPa. The method they used was to force steam over some crushed mineral, which was small enough to pass through one filter screen but not the second screen. All of this occurred in an isothermal heated bomb. The concentration of the mineral that dissolved between the two screens was considered to be the solubility limit for the temperature of the bomb. After the bomb, the steam was condensed and weighed to measure the concentration of the dissolved mineral. For sodium sulphate, they determined several solubility points at 500 °C, and various pressures. If a linear interpolation is completed between points at 13.3 and 66.6 MPa, a concentration of 0.0084 wt% is determined for 25 MPa (figure 2.4). Ravich and Borovaya (1964), and Martynova and Samoilov (1962), completed phase equilibria studies for some inorganic compounds in sub- to near critical water. The apparatus used by Ravich and Borovaya (1964) consisted of an autoclave (sealed pressure vessel) which measured the pressure drop associated with the dissolution of the crystalline salt. This was achieved by heating an aqueous solution of salt in the autoclave and when the appropriate temperature and pressure was reached, the autoclave was tilted so that salt tablets in a holder came in contact with the solution. If the solution was unsaturated, some salt would dissolve leading to a contraction of the system resulting in a decrease in pressure. If the solution was supersaturated, relative to the conditions in the autoclave, no dissolution would occur, and the system pressure would remain the same (salt above the saturation point would precipitate out during the heating). In using the autoclave, Ravich and Borovaya (1964) discovered that as the critical temperature was approached (and the solubility limit decreased rapidly), the pressure drops associated with the small amount of salt dissolving were not measurable. Therefore, the results for solubility of sodium sulphate that they determined were at sub-critical temperatures (figure 2.4). Chan et al. (1994) at Sandia National Laboratories conducted solubility experiments with a SCWO pilot plant running at 0.036 kg/min A 0.5 wt% solution of 20 510 i a. a H 310 l.E-07 l.E-05 l.E-03 l.E-01 l.E+01 l.E+03 Concentration [wt%] © Chan et. al (1994) A Interpolation of Martynova (1973) A o Ravich and Borovaya (1964) x Morey and Hesselgesser (1951) - Solubility Eq. (Chan et aL, 1994) Armellini and Tester (1992) Figure 2.4: Summary ofprevious data on the solubility of sodium sulphate in water. Chan et al. 's (1994) data was taken at 27 MPa and Morey and Hesselgesser's (1951) data point was interpolated between pressures of 13.3 and 66.6 MPa. All other data points are for 25 MPa. 21 sodium sulphate in water was heated to a known temperature in the reactor. When the concentration flowing through the reactor dropped below the solubility limit, it was assumed that all salt in excess of the solubility limit would precipitate leaving a saturated solution. The effluent was cooled and analyzed for Na+ ions by specific ion electrode to determine the concentration. The last 600 cm of the reactor was kept isothermal within several degrees Celsius. From these experiments the following equation was determined: 326.62-Th fdeg.CJ C s a t =/0 J5.S3 (2.8) where C s at is concentration [wt%] of the solubility limit for a given temperature. The results are also displayed in figure 2.4. At the Massachusetts Institute of Technology (MIT), Armellini and Tester studied phase equilibria of both sodium chloride and sodium sulphate. They used two different methods to examine the temperature-pressure behaviour of salt water systems. The first method used pure deionized water which flowed over a isothermal salt bed. The water was assumed to dissolve enough salt while flowing over the salt bed to become saturated. The samples were analyzed for the dissolved ions (Na+, CI") to determine effluent concentrations. The second method used an optical test cell in which static (non-flowing) isobaric salt formation experiments were performed for NaCl and Na2S04 at 250 bar. The solubility study of Na2S04 at M.I.T. provided unsteady effluent measurements. An average taken yielded only one data point as 0.9 ppm ± 0.2 ppm at 500 °C and 250 bar. In two of the optical-cell experiments with sodium sulphate, solid nucleation was observed during heating. The solid salts appeared at fine particles which settled in the cell, and salt crystals which grew on the inside window surface (Armellini, 1993). A sodium sulphate solution in water appears to have no liquid phase present at 250 bar. In fact, the salt precipitates out directly as a solid as the mixture is heated past the solubility limit. 22 It is obvious from the results for solubility of sodium sulphate in water (figure 2.4) that there is a large discrepancy in the literature, especially around the critical region. However, many different methods were used for the solubility studies. This could be one of the reasons for the large difference in measurements. It is interesting to note that Chan et al.'s (1994) measurements and derived solubility equation predict a linear (log scale) dependence through the critical point which is not the trend that has been previously documented (Tester et al., 1991). Unfortunately there has not been much work completed with sodium sulphate, so the reliability of the data, especially at higher temperatures (lower concentrations) is questionable. However, fouling studies with this salt (due to the precipitation of a solid) would be facilitated, if a complete phase diagram was available. Sodium chloride's phase diagram has been documented in the past, and the results from previous experiments are consistent with Armellini's data (figure 2.5). It is quite complex with the existence of several different phases (vapour, liquid, and solid). At 387 °C the mixture lies on the critical solution point, where vapour and liquid phases are identical. With increasing temperature the mixture reaches a three phase equilibrium at 450 °C. Above this temperature the salt-water system predominantly exists as a vapour-solid region, with a very low concentration of supercritical fluid (less than 0.02 wt%). Sodium chloride's phase diagram indicates that any fouling process involving NaCl would be complex with a liquid phase forming before solids deposit on the tube walls. The most interesting part of these results was that if chlorine concentration is used to calculate the solubility of NaCl (Martynova and Samilov, 1962), then the measured solubility will be high, due to the hydrolysis of solid NaCl: NaCliy) + H20 = NaOH(t) + HCl{v) (2.9) Therefore HQ would be another source of chlorine concentration in the vapour phase. The extent of this reaction was not given, but if any studies are to be done with NaCl in the future, pH measurements should be taken concurrently with chlorine concentration or conductivity to determine how much HC1 is present. 23 390 370 350 0.01 one phase fluid region + 0.1 1 10 Concentration NaCl [wt%] Armellini (1993) Olander and Liander (1950) Sourirajanand Kennedy (1962) Armellini estimated fromLinke (1958) BischoffetaL (1986) Compilation of Bischoff and Pitzer (1989) 100 Figure 2.5: Phase diagram for the system of sodium chloride and water at 25 MPa. 24 2.5.2 Kinetics of Salt Nucleation and Deposition Determining the solubility of salts in supercritical water is only one aspect of the salt deposition problem. Once the solubility limit is exceeded by a salt solution, the salt can heterogeneously nucleate on the deposition surface, nucleate and deposit as particles, and deposit through molecular diffusion. Studies have been completed examining various areas of salt nucleation and deposition with both sodium sulphate and sodium chloride. 2.5.2.1 Salt Nucleation Studies At MIT. studies on salt nucleation experiments were completed by Armellini and Tester (1991). The experiments involved injecting a cool (100 - 140 °C) salt solution through a nozzle into a supercritical water (SCW) feed to facilitate rapid or 'shock-like' crystallization of the dissolved salt (figure 2.6). The process was viewed through an optical cell designed for temperatures up to 600 °C and pressures of 40 MPa, which used sapphire windows as the view ports. The experiments injected various concentrations of both sodium sulphate and sodium chloride solutions into the SCW feed. The cell was kept at 25 MPa and had a constant cell-block temperature of 600 °C. Two different areas were examined through the window, the initially mixed region, immediately after the nozzle, and the fully mixed region, when the nozzle tip was positioned at the top of the cell, 5.7 cm away from the window. Photographs of the experiments were taken through the window using a high-speed camera, with illumination from behind with white light. In the initially mixed region, a colder pure water feed injected through the nozzle was seen as a darker stream against the SCW due to the density differences. The 3.0 wt% NaCl solution had similar appearances as the pure water feed. However, the 3.0 wt% Na2S0 4 jet and surrounding solution appeared much darker. This was probably due to the nucleation of small salt particles that scattered the light. In the fully mixed region again no difference was noticed as the pure water feed was switched to a 3.0 wt% solution of NaCl and water. The cell was cooled and opened to reveal small white particles covering the bottom 25 Salt Solution sew t Feed Window View Nozzle Temp. Thermocouple Location Water Cooled Nozzle 7 Mixed Temp. Thermocouple Figure 2.6: Schematic of cell interior during the flow/shock crystallization experiments. Adaptedfrom Armellini and Tester (1991). surface. These were thought to be homogeneously nucleated particles with lengths between 10 and 100 um (determined from scanning electron microscope (SEM) photomicrograph). The 3.0 wt% Na2SC«4 solution became clouded in the fully mixed region, and when the cell was cooled, small white particles had deposited on the bottom of the cell. At first the sodium sulphate deposits seemed to have fairly large particle sizes, but at high magnification, SEM photomicrographs revealed that the deposit was composed of many small particles (1-2 nm) fused together. The different phase behaviour of NaCl and Na2S04 provides a possible explanation for the difference in photographs for the initially and fully mixed regions during the experiments. With sodium chloride, initially liquid droplets were formed, which became unstable as the three-phase equUibrium temperature (450 °C) was reached (as the jet was 26 heated by the SCW feed). This led to formation of relatively large solid particles that had amorphous morphology. For sodium sulphate, direct precipitation of a solid occurred as there appears to be no vapour-liquid region at 25 MPa. With the size of nucleated particles so small (1-2 u.m), the number formed was quite large, scattering the white light and producing the cloudy image taken by the camera. i 2.5.2.2 Deposition Rates from a Sodium Sulphate Solution Also at M.I.T., Hodes et al. (1997) conducted experiments and modelling which examined the deposition rate of sodium sulphate onto a heated cylinder for supercritical conditions. Flow was directed through a 1.91 cm Swagelok cross (figure 2.7) which was machined to fit sapphire windows in the male connectors. The heated cylinder or 'hot finger' was fabricated from Hastelloy C276 and is 2.76 cm in length and 5.08 mm in diameter. A cartridge heater is inserted into the cylinder which dissipates approximately 10.61 W of power. The cylinder was instrumented with five 0.254 mm diameter, Inconel sheathed, type K thermocouples. The entire cell can be kept isothermal with four cartridge heaters. The experiments used a 4 wt% sodium sulphate and water solution flowing at 0.0105 kg/min over the cylinder with a bulk fluid temperature of 355 °C and a pressure of 25 MPa. The heated cylinder increased the local temperature of the solution (various surface temperatures above 355 °C), and this limited deposition to the cylinder surface. Once deposition had occurred for several minutes, the system was purged with nitrogen and cooled, after which the 'hot finger' was removed. The salt deposits were then weighed and examined. Modelling of the deposition involved heat and mass transfer calculations, which used local Nusselt and Sherwood numbers for a vertically oriented, isothermal, and constant concentration flat plate (Gebhart and Pera, 1971). For the mass transfer modelling it was assumed that no nucleation occurred in the bulk fluid. Instead, the dissolved salt traveled to the salt-layer solution interface by molecular diffusion, and heterogeneously nucleated. Diffusion coefficients for Na2S04 were estimated from data 27 1 Thermocouple • Hot Finger: Window Figure 2.7: Schematic of the 1.91 cm (inner diameter) Swage lok cross used for the deposition experiments on the heated cylinder ('hot finger'). Sapphire windows can be placed in any of the shaded ports. Flow is in and out of the page. Adaptedfrom Nodes etal. (1997) for NaNO-3 in SCW (Butenhoffet al., 1996). The results of the experiments indicated a deposition rate on the order of 0.1 g/min on the heated cylinder. Model predictions for mass deposited on the cylinder were a factor of three lower than the experimental data. Increasing the diffusion coefficient by a factor of four resolved the difference. Additionally, the surface temperature on the cylinder increased as the salt layer grew, due to the thermal resistance of the sodium sulphate deposits. It was thought that a large part of the discrepancy between the model predictions and the experimental data was due to the uncertainty in the thermodynamic and transport properties of sodium sulphate. 28 2.5.2.3 A Simple Salt Deposition Model In Livermore, California at Sandia National Laboratories, the experimental work supervised by Rice focused on fouling a tubular reactor with sodium sulphate (LaJeunesse et al., 1993; Chan et al., 1994). The tubular reactor was 750 cm long, with two 90 turns at 260 and 300 cm and made from Inconel 625. The tube's dimensions were 1.43 cm O.D. and 0.48 cm ID. The experiments used a sodium sulphate solution of a known concentration which was fed through the system until the deposits completely blocked the flow or "plugged" the tube. This time period was referred to as the 'plugging time' ( tp). The 'plugging time' was determined by using two sets of differential pressure transducers along the reactor length. When a pressure excursion of 7 MPa above the baseline pressure of 25 MPa was noticed the tube was considered plugged in the region of the differential pressure transducer. A series of 'plugging times' were recorded for different mass flows and temperature profiles of the reactor. The data taken during experiments was then compared to a simple salt deposition model. The salt deposition model used the solubility equation (equation 2.8) derived from the solubility experiments. The salt deposition model assumed that as a salt solution was heated, everything above the solubility limit deposited immediately on the tube walls. With the deposition rate defined by the solubility limit, plugging times could be calculated (refer to Chan et al., 1994, for details). Several experiments were completed to compare to the model predictions and the results are contained in Table 2.3: Table 2.3: Comparison between model and experimental data (Chan et al, 1994) Test No. Flow rate [g/s] Temperature tp Measured tp Calculated Profile [minutes] [minutes] 1 0.6 gradual 48 49.1 2 0.6 gradual 41 49.1 3 1.2 gradual 23 24.5 4 1.5 gradual 37 19.6 5 0.6 steep 28 23.0 29 The results indicated that at low flow rates of 0.6 g/s (test no. 1,2 and 5), the model compared well with the experimental plugging times. However, it should be noted that based on the experimental work that is contained in the present study, the solubility equation Chan et al. used appears false. So the results from their experiments are not easily interpreted. The comparison between experimental and model results would indicate that the precipitated salt was either depositing on the walls as particles very close (axial location) to the nucleation site, or that molecular diffusion to the walls was extremely rapid. These results using the wrong solubility equation implies that their temperature errors were large, or they used the equation differently than is described in the paper (Chan et al., 1994). Chan et al.'s experiments were run at low mass flows compared to the conditions (18.5 kg/min) that are used in the only commercial facility in Austin, Texas. Their salt deposition model did not incorporate any deposition mechanisms (they assumed all salt above the solubility limit deposited), which makes it difficult to scale up the model for larger facilities. A model which includes deposition mechanisms for the salt must be developed. This model should include molecular and particle deposition rates, and be applicable to higher flow rates. 30 3. Computer Model of Heat Transfer and Salt Deposition 3.1 Overview A program (SCHeat.f) was written to model the heat transfer to a solution of Na2SC«4 - H 20 in a tube through the critical region. Properties and parameters were evaluated as small steps were taken axially along the heated tube. Fluid thermodynamic and transport properties are for pure water. A Nusselt number correlation was used to obtain heat transfer coefficients and develop temperature profiles. Four salt deposition models were also incorporated into the program for subsequent comparison with experiments. All models assumed no surface resistance to attachment of salt molecules and/or particles. In one of the models, it was assumed that particles would nucleate instantly and grow rapidly to a diameter of 2 um. Another of the models assumed that nucleation was inhibited. The salt layer thicknesses were inferred from outside surface temperatures (which increased where salt deposited). This was done because direct measurements of the layer would have required cooling the system with nitrogen (Armellini, 1991) so the deposits would not re-dissolve, as well as disassembling the test section to gain access to the inner tube surface. Peak heights of the salt layer were important for determining how quickly a tube will completely 'plug' closed. The effect of the salt layer roughness was not considered in the heat transfer calculations. The following chapter describes the calculation of the thermodynamic and transport properties of water, and the procedure used to predict the temperature profiles. Then, the assumptions made in the salt deposition program are outlined and the calculations used to model the deposition rates are explained. 31 3.2 Heat Transfer Program The heat transfer program calculates bulk, inner wall, and outside wall temperatures for a sodium sulphate - water solution flowing through a tube with a constant heat flux applied to the wall. 3.2.1 Thermodynamic and Transport Properties of Water The first step was to enable the program to determine the properties of water at any given state. A program called EQTEST.f (Pruss and Wagner, 1994) was used to determine the thermodynamic properties of the water at the given temperatures and pressures and was attached to the main body of the heat transfer program (SCHeat.f). EQTEST.f requires either a temperature-pressure or temperature-density point as the input, and calculates the other thermodynamic properties (e.g. enthalpy, specific heat capacity, entropy, etc.) for that state. The transport properties, viscosity and thermal conductivity, were determined by interpolating in the NBS NRC steam tables (Haar et al., 1984) (the tables are tabulated in only 25 degree increments). Originally a curve fit was applied to the steam table data for the transport properties, but this correlation proved to be very inaccurate, especially around the critical point. Once the thermodynamic and transport properties could be evaluated, the next step was to model the increase in bulk fluid temperature (due to an applied heat flux), with an energy balance. 3.2.2 Energy Balance Several initial conditions had to be specified for modelling the heat transfer. The tube diameter d was required, the mass flow rate /w[kg/min], the heat flux q [kW/m], the bulk temperature Tb of the fluid, and the pressure P [MPa]. With the bulk temperature of the fluid, the enthalpy Hx [kJ/kg] of the fluid was found using EQTEST.f. For a given length of tubing Az [m], the enthalpy H2 [kJ/kg] at 32 the end of that section was determined using the heat flux (assuming perfect insulation so that all of the heat was transferred to the fluid) and the following equation: q Az H2=Hl+?— (3.1) m With the second enthalpy known, the new bulk temperature was calculated using EQTEST.f. Using the bulk temperature, the transport properties were determined from the tables and the Reynolds Re and Prandtl Pr numbers were then calculated. With this step-wise method, the bulk properties for the entire length of tube were determined (figure 3.1). Cross Section of Tube Heat Flux Flow Az Initial conditions: Thermodynamic and transport properties • After step Az • Energy balance to get new bulk temperature • New thermodynamic and transport properties Figure 3.1: The step-wise method of the heat transfer program SCHeat.f 33 3.2.3 Predicting the Inside Wall Temperature The first step in predicting an inside wall temperature was to calculate a heat transfer coefficient. In order to determine the heat transfer coefficient, a Nusselt number correlation (Swenson et al., 1965) for supercritical water flow in tubes was used (outlined in section 2.4). The Nusselt number correlation requires properties at the inside wall for an accurate prediction. An initial estimate of wall temperature was made using bulk properties with the Swenson et al. correlation (equation 2.4) and the following equation: r--r>-»£ ( 3 2 ) where q2 is the heat flux per unit area [kW/m ]^. With this temperature difference a wall temperature Twi was calculated. An iterative procedure was devised (figure 3.2) so that the Nusselt number correlation was used effectively with the wall and bulk properties. The properties were evaluated at the wall temperature r w i . The Nusselt number was recalculated using bulk and wall (at Twi ) properties. The new Nusselt number Nu2 and thermal conductivity HT^) produced a second calculation of (T^-T^i . The second temperature difference determined another wall temperature TV2 which was used to repeat the process until two successive T^-Tb values were approximately equal (less than 0.01 °C difference). When compared to the original calculation of Tw , the final value of the iteration was within 1 or 2 °C. 3.2.4 Predicting the Outside Wall Temperature Due to the fact that experimental measurements of temperature will be made on the outside surface of the tube wall, it was necessary to model the outside wall temperature Te using the inside wall temperature. Additionally the tube wall will have 34 Swenson et al. Nii\ with bulk / wall properties (no wall first time) Userw 2 for wall properties Calculate (rw - 7b)i JE Calculate Wall Properties 1 r Calculate new Nui based on bulk / wall properties Calculate new (Tw - 7b)2 Figure 3.2: Flowchart describing the iterative procedure used in calculating the inside wall temperature with an initial Nusselt number estimate with only bulk properties. 35 internal heat generation, so the differential equation for the heat conducted through the wall is given by: d f dT] 2q2A2r drKrk^dr)=-ri(l-A2) ( 3 3 ) where r is the radial distance from the centre of the tube [m] Atube is the thermal conductivity of the Inconel tube wall [W/K-m] rx is the inside tube radius [m] and A =r\/r0 Since the thermal conductivity of the Inconel 625 (material of tube) is only weakly dependent on temperature, it was assumed to be constant over the tube wall thickness. It was also assumed that the outside of the wall was perfectly insulated. Therefore the boundary conditions for the tube were: at r = rilA T = Te the measured external wall temperature [K] dTldr = 0 perfectly insulated (adiabatic) The solution of (3.3) with the given boundary conditions produces a temperature difference: T ?2 r i w ~ 2k f A2 A -ln(A )-l w V 1-A' (3.4) and K, was evaluated at rw . Using this method, with a known bulk temperature the inside wall and outside wall temperatures were calculated at each step Az . This enables the program to produce an axial temperature profile for the entire test section. Comparisons of the Nusselt number correlation's predictions of inner wall temperatures 36 (and consequently outside wall temperatures) and experimental data are discussed in section 5.2.2. Once the program was capable of generating temperature profiles for pure water in the test section, the next task was to develop a procedure to model the deposit of sodium sulphate on the inner walls of the tube from a salt solution. 3.3 Salt Deposition Program There were two reasons for modelling the salt deposition in the SCWO system. The first was to aid in the design of the test section, by indicating what measurements would be important in determining the conditions and thickness of the salt layer. The second was to create several different models, which focused on different deposition mechanisms. Comparison of these models to the experimental data would give an indication of which mechanisms were dominant. The program for salt deposition was incorporated with the heat transfer section. 3.3.1 Molecular Diffusion Rates In order for salt to deposit on the tube walls, it must first be transported from the bulk fluid. There are two distinct mechanisms which enable salt to reach the wall surface. The first is molecular diffusion and convection, or transport of single salt molecules. The second is particle deposition, from salt particles that have nucleated in the bulk fluid. The case of molecular diffusion was considered first. There are many similarities between the governing equations for heat, momentum and mass transfer. The momentum and energy equations of a laminar boundary layer, for incompressible steady flow, with constant properties and constant pressure are defined by: 37 du du ju d2u dz dy p dv: u — + v — = -_— (3.5) dT dT d2T —+ v —= a—: dz dy dy1 u  + v -^ 77 =  -7-y (3.6) where u is the mean fluid velocity in the z-direction [m/s] v is the mean fluid velocity in the y-direction [m/s] p /p is the kinematic viscosity [m2/s] a is the thermal difrusivity [m2/s] For convection heat transfer problems, the dimensionless group called the Prandtl number (equation 2.6), which is the ratio of p. / pa , links the two equations. To examine the relationship between the energy and momentum formulations and mass transfer another equation was needed. If diffusion was occurring in the boundary layer due to a concentration gradient, an equation for concentration of the diffusion species similar to the energy and momentum equations could be developed: dCh, dC\ where C A is the concentration of species A diffusing through the boundary layer D is the diffusion coefficient [m2/s] The solution to equation 3.7 will be similar in shape to the velocity (momentum) profile (equation 3.5) when p. = pD , or p I pD = 1. This dimensionless ratio is called the Schmidt number: 38 (3.8) which is an important number when convection and mass transfer are significant factors in the process involved. To create similar temperature (equation 3.6) and concentration profiles (equation 3.7), the condition a = D, or a ID - 1 must be met, and this ratio is called the Lewis number: Le = — = D Dcvp (3.9) which is important when heat and mass transfer are occurring. The similarities between all three governing equations suggest that a mass transfer coefficient hm [m/s] could be analogous to a heat transfer coefficient in form, with the heat transfer coefficient a function of Reynolds and Prandtl numbers. hd . x — = f(Re,Pr) (3.10) and the mass transfer coefficient a function of Reynolds and Schmidt numbers. ^ = f(Re,Sc) (3.11) 39 Continuing with the analogy between heat and mass transfer, the mass transfer coefficient can also be expressed in terms of the friction factor / . This is similar to the heat transfer coefficient equation which uses the Reynolds analogy (Holman, 1981) relating the heat-transfer rate to the frictional loss for tube flow: » f = „ (3.12) uc p 8 However, the heat-transfer-fluid-friction analogy for laminar flow over a flat plate indicated a Prandtl-number dependence of Pr2'3 . It has been shown that equation 3.12 can be applied to turbulent flow over a plate and also turbulent flow in a tube with the modification (Holman, 1981): Pr2/3=4 (3.13) ucp p 8 and this is called the Reynolds-Colburn analogy. Substituting for the mass transfer coefficient and replacing the Prandtl number with the Schmidt number the equation becomes: K Sc2/3 U I 8 (314) For the condition of the salt deposition experiments when both heat and mass transfer are occurring simultaneously, the heat and mass transfer coefficients were related by dividing equations 3.13 and 3.14: 40 This mass transfer coefficient does not take into account the large property variation from the bulk fluid to the wall. Since the Nusselt number correlation (equation 2.4) used in the program accounts for the wall to bulk property variations, a mass transfer correlation was developed, using a similar method that was used to derive equation 3.15. The mass transfer coefficient and Schmidt number were substituted into equation 2.4. The result was a Sherwood number Sh correlation: Sh = h^l = 0.00459 Re0923 ['HSLLBSL D N 0.613 f \ 0.231 Av w J (3.16) dividing equation 3.16 by equation 2.4 produces the relation for heat and mass transfer: i h. m ~ o V Le 0 3 8 7 (3.17) This mass transfer coefficient uses an integrated heat capacity, and has a different power for the Lewis number than equation 3.151. Also all properties were evaluated at the wall temperature (where the diffusional properties are more important). The dependence of equation 3.17 on the Lewis number, results in a dependence on the diffusion coefficient. For sodium sulphate, the diffusion coefficient had not been experimentally determined, so an estimate had to be made. For practical purposes the molecular diffusion coefficient was calculated from the Stokes-Einstein relation (Shaw et al., 1991): 1 Model predictions which used a different power on the Lewis number in equation 3.17 are contained in Appendix C. This was done to check the sensitivity of the model predictions for a modified mass transfer coefficient. 41 D = 3n^ d, (3.18) where fa is Boltzman's constant [J/K] dm is the molecule diameter [m] In order to use equation 3.18, the molecular diameter for sodium sulphate was needed. Initially a basic analysis was completed to calculate the diameter. The density of sodium sulphate is 2.68 g/cm3 (Lide, 1993), and the molar mass is 142 g/mol. The number of molecules in 1 cm3 will be: N ( g \( 1 mol) 2.68-^r V cm* J V142 g J 6.023 X JO 23 mol = 1.1367 X 10 22 (3.19) where N is the number of molecules. If each molecule is assumed spherical the volume is: (3.20) where V is the molecule's volume [m3]. If it is assumed that all of the volume space in a cubic centimetre is occupied by sodium sulphate molecules, the maximum diameter can be calculated: 3\6 1 cm _R dm = I = 5.52 X 10 8 cm *m n N (3.21) 42 To verify the accuracy of the molecule diameter, experiments with sodium sulphate by Hodes et al. (1997) were examined. Hodes et al. (1997) used the diffusivity coefficient (0.25 x 10'7 m2/s) for sodium nitrate (ButenhofT et al., 1996) in their calculations with sodium sulphate. The bulk temperature of the fluid in their experiments was kept constant at 355 °C. With these values and equation 3.18, a molecule diameter of 5.27 x 10~8 cm was determined. This value was similar, but below the maximum dm calculated in equation 3.21, and appeared acceptable. Subsequently a dm value of 5.27 x 10~8 cm was used for diffusion coefficient calculations at higher temperatures. Using the mass and diffusion coefficient, the overall mass transfer rate was defined. The mass transfer rate depends on both the mass transfer coefficient and the concentration difference (dissolved salt) between the bulk and wall conditions: where C\ is the dissolved salt concentration in the bulk [wt%] C w is the dissolved salt concentration at the wall [wt%] / M m o i is the molecular diffusion rate [kg/s] Equation 2.22 assumed that there was no surface resistance to the attachment of salt molecules. With equation 3.22, the mass deposited due to molecular diffusion was calculated at each step in the program. With very little known about the actual mechanisms that are occurring in salt deposition, three separate models were developed that used different combinations of both molecular and particle deposition for predicting the growth of the salt layer. A fourth model was also incorporated into the program which was identical to a model developed by Chan et al. (1994) at Sandia. (3.22) 43 3.3.2 Model 1: Suspended Particles In this model (figure 3.3) it is assumed that particles nucleated in the bulk fluid when the bulk solubility limit dropped below the concentration of the salt solution. The new particles did not deposit on the walls due to their low diffusivity but instead were transported along with the bulk of the fluid. In this case, the only deposition resulted from the transport of single salt molecules. When the solubility limit at the wall was exceeded by the concentration of the solution, salt molecules diffused to the walls (due to the salt concentration difference between the bulk and wall fluid) where they deposited on the inside wall surface. To understand the parameters that influence Model 1, the differential equations governing the concentrations of particles and dissolved salt are examined. For this model there were two conditions: the dissolved bulk concentration was less than the solubility limit ( Cb < Csat) or the dissolved bulk concentration was equal to the solubility limit ( C \ = C M t )• For model 1 the concentration of the bulk particles Cbp varied with the solubility limit (which was decreasing with increasing temperature) and the concentration of salt that diffused to the walls C m o i : forCh<Ct sat dC bp dz dCsat dTb _dCmo\ dTb dz dz (3.23) forCh=Ct sat where C m o l = ^ f f i 2 L x 100% (3.24) m and -^- = -3— (3.25) dz mcp 44 Beginning of Step Calculations During Step End of Step First Stage Second Stage Cbi Dissolved Solid Salt Cbpi Dissolved Salt Above Solubility Limit Nucleates as Particles in , the Bulk Increase in Particle Concentration Molecular Diffusion Deposition No Particle Deposition Az -b2 -bp2 Figure 3.3: Schematic diagram of the salt deposition mechanisms occurring in one length-step for Model 1: Suspended Particles. 45 was the axial temperature gradient due to a constant heat flux. The concentration of dissolved salt also depended on the solubility limit and molecular diffusion rate: dC± dz dC mol dz forCb<C sat (3.26) ^sat dTb dTh dz forCh=Ct sat 3.3.3 Model 2: No Nucleation The second model (figure 3.4) was very similar to the first except that we assumed there was no bulk nucleation of particles. If the solubility limit dropped below the concentration of the fluid, the solution became supersaturated. Again, deposition occurred through molecular diffusion, but since the dissolved salt concentration of the bulk was much higher than in Model 1, Model 2 should exhibit an increased mass flux of salt to the tube wall. For Model 2 there is no particle nucleation so the concentration of dissolved particles depended on only the molecular diffusion rate: dC* dz dC, mol dz (3.27) 3.3.4 Model 3: Chan et al. (1994) The third model (figure 3.5) considered was identical to that developed by Chan, et al. (1994). When the bulk solubility dropped below the concentration of the solution, all salt above the solubility limit deposited on the tube walls. Deposition occurred at the 46 Beginning of Step Calculations During Step End of Step *-bl Dissolved „ . . . Molecular Solution can be . _ j j Diffusion Supersaturated _ r Deposition *-b2 Solid Salt Cbpi = o No Bulk Particle Nucleation 4 » Cbp2 = 0 Az Figure 3.4: Schematic diagram of the salt deposition mechanisms occurring in one length-step for Model 2: No Nucleation. 47 Beginning Calculations During Step End of Step of Step Cbi -Solubility Limit at Tbuik Dissolved All Salt Above Solubility Limit Deposits Immediately Cb2 = Solubility Limit at Tbuik In this Model it is not Specified Whether there is Particle Nucleation Before Immediate Deposition Az Figure 3.5: Schematic diagram of salt deposition mechanism occurring in one length-step for Model 3: Chan et al. (1994). 48 same axial location as the precipitation (i.e. there was no transport along the tube). The salt concentration in the bulk then duplicated the solubility limit. In Model 3 the difference in solubility between two successive increments Az along the test section, was assumed to have created deposits on the tube walls. Therefore the bulk concentration was described by: dCy, dC^t dTu ^ — 5 - (3.28) dz dTy> dz 3.3.5 Model 4: Complete In the final model (figure 3.6), the molecular diffusion rate calculated was identical to Model 1. Additionally a particle deposition rate was incorporated which used an experimentally determined deposition velocity. Papavergos and Hedley (1984) examined the deposition of particles from a turbulent flow stream to an adjacent surface. They did a comprehensive review of previous experiments mainly involving deposition of aerosol droplets entrained in duct air streams. Data for particle deposition in liquid streams would be more accurate, but more experiments have been conducted with aerosol droplets due to operational convenience and low cost. The droplet sizes that were considered were larger than those influenced by molecular diffusion, but small enough so that gravitational effects were negligible. The particle size of the sodium sulphate precipitate was found to be 1 - 3 p.m (Armellini and Tester, 1994) and was in this range. It was realized that the experimental data used in this review did not cover near critical temperatures, where the bulk and wall properties are quite different. However, in the absence of deposition rates for particles in the critical region, the results from the review were implemented in the model. 49 Beginning Calculations During Step End of Step of Step First Stage Second Stage r . r , „ Dissolved Solid Salt c -1 Dissolved Salt 1 Above Solubility | Limit Nucleates . | as Particles in . the Bulk Increase in Particle Concentration Molecular Diffusion Deposition Deposition Velocity for Particle Deposition *-b2 C. -t-bpl 4 » *-bp2 Az Figure 3.6: Schematic diagram of salt deposition mechanisms occurring in one step for Model 4: Complete. 50 For the purpose of describing deposition rates, Papavergos and Hedley (1984) fit a deposition velocity to experimental data for horizontal flow systems: Vd=Vd+u (3 29) where Vi is the particle deposition velocity [m/s] Vi is the dimensionless particle deposition velocity [-] u is the wall friction velocity of the fluid [m/s] 0.065 (Sc) -2/3 for rp+ < 0.2 3.5 x 10~4 (rp+)2 for 0.2 < r p + < 20 O.J 3 forrp+>20 (3.30) where Zp + is a dimensionless particle relaxation time: (331) where tp is the particle relaxation time [s]: 51 _ Aalt dp2 rp~ 18p (3.32) where fan is the density of the salt particle [kg/m3] a\ is the diameter of the particle [m]. It was assumed that nucleation was instantaneous with rapid growth to a size of 2 urn (Armellini and Tester, 1994). The wall friction velocity u of the fluid can be determined by: « u = (3.33) where rw is the wall shear stress [N/m ] pu2f T w = 8^ ( 3 3 4 ) Once the deposition velocity was calculated, it was substituted for the mass transfer coefficient in equation 3.21 to determine a mass transfer rate mpait for the bulk nucleated particles: m part = VA n d Az p (C -C '-bp ^bpw 100 (3.35) where Cbpw is the concentration of particles at the wall ( = 0). In this case it was assumed that all particles that reached the tube surface became attached. Now the differential 52 equations for Model 4 can be described in terms of a particle deposition concentration Cpart and molecular diffusion terms: dC bp dz — < dTu dz dz dz for C b < C s a t forCh=Ct sat (3.36) where Cpart = X 100% (3.37) However the concentration of dissolved salt remains the same as in model 1: dz dC, mol dz dCs&t dTb dTh dz forCb < C s a t (3.38) forCh=Ct sat 3.3.6 Salt Layer Growth Rate With the four different fouling rates from the salt deposition models, the salt arriving at the wall had to be converted to a salt layer. It was assumed with all models that any salt reaching the inside wall of the tube formed a layer of salt. The deposition rate was related to the thickness of salt by: ^sa l t_ "salt ( 3 3 9 ) 53 where y^u is the thickness of salt [mm] TMsaU is the deposition rate of salt (either molecules, particles, or both) [kg/s] t is the fouling time [s] Recent work by Hodes et al. (1997) at MIT. has indicated that the density of 2680 kg/m3 (Lide, 1993) may not be correct in determining a salt layer thickness. Their experiments involved the deposition of sodium sulphate on a heated cylinder at near to supercritical conditions (see section 2.5.2.2), and the salt deposits formed on the cylinder had a porosity factor from 82 to 71 %. The porosity <j> was defined as: where Vj is the total volume of salt including voids (stagnant water) [m ] Vs is the total volume of the salt [m3] The lowest porosity value (71%) had the longest fouling time (11.92 min.) and was used with the following equation: to calculate an effective 'salt layer density' #a y e r of 777.26 kg/m3, which was used in equation 3.39. This 'salt layer density' neglects the water in the pores, but is accurate for determining the rate of salt layer growth. Equation 3.39 also indicated that the surface area for deposition decreases with the salt layer thickness. A correction was made for the decrease in diameter as the salt layer grew. A time-step was incorporated into the program which divided the total fouling time into 10 periods. The program initially runs through the entire tube length for 1/10 of the fouling time, and stores the location and (3.40) (3.41) 54 thickness of any salt deposits (figure 3.7). A new diameter *4ui = d - 2 yian [m] was calculated where ever salt was deposited in the first time-step, and used for all heat transfer and salt deposition calculations. Additionally, in the fouled region, another temperature T„ was calculated at the surface of the salt layer in contact with the fluid. The calculations of increased wall temperatures and total salt mass, which are needed for experiment interpretation, are discussed in section 5.4.4. 3.3.7 Model Implementation The program was written in FORTRAN-77 and complied on a Pentium, 75 MHz personal computer. The time period for modelling one experimental run, with one salt deposition model was approximately 20 seconds on this platform. The source code with examples of input and output data files is contained in Appendix C. 3.4 Preliminary Conclusions from the Program The model was used to generate temperature and salt deposition profiles for different cases of heat flux, mass flow, and initial salt solution concentration (Teshima et al., 1997). Model 3 was also compared to a similar model by Chan et al. (1994). As mentioned earlier, measurements at Sandia were most consistent with a simple model in which salt deposition is instantaneous. However, the accuracy of this model was much less as their flow rates were increased to 0.09 kg/min. At UBC we will be working with higher flow rates (1 kg/min), and it was necessary to evaluate other salt deposition mechanisms. The pressure profiles generated by the salt deposition model indicated that there was a measurable pressure drop (on the order of kPa). However, locating the salt deposition will be difficult. Appreciable fouling was occurring in 1 hour, so fouling experiments are realistic. Additionally, by varying parameters such as heat flux and mass flow, the salt deposition profile could be manipulated to create the most desirable results. 55 Cross Section of Tube Total Fouline Time =At 10 At 2 At i FlOW f1r , dfoui r Az k : Salt Layer Grows with Each Time-Step At Each Length-Step in the Fouled Region df o u i Will Be Differenct Figure 3.7: Outline of time-step implementation in the program for correction of decreasing tube diameter and deposition surface area. 56 for the experiments. This implies that in an actual SCWO pilot plant, the proper control of these process variables could be used as a prevention technique for salt deposition The preliminary modelling aided in the design of an experimental test section, which was designed to measure temperature profiles and pressure drops. 57 4. Experimental Apparatus The SCWO system was constructed to perform solubility experiments (for comparison to previous experimental work on the solubility of sodium sulphate in water), and salt deposition experiments (to verify or disprove the models). It was designed to operate at the high temperatures and pressures of supercritical water. In the following chapter, the SCWO system design and safe operation is described. Included are sections on the instrumentation used for experiments and its incorporation into the SCWO facility, and the data acquisition system. 4.1 The SCWO System The SCWO system (figure 4.1) is composed of approximately 23.2 m of Inconel 625 high pressure tubing (0.622 cm ED and 0.952 cm (3/8 ") OD). The system includes the following sections: Regenerative Heat Exchanger: 6.2 m in length Preheater 1: 4.7 min length Preheater 2: 4.7 m in length Test Section: 3.8 m in length Outlet of Test Section to Heat Exchanger: 3.8 m in length Process Cooler: 6.2 m in length, 0.952 (3/8 ") stainless steel The system was divided into sections so that it could be disassembled for maintenance and also allow the addition of new subsystems. All sections are joined together with unions designed by NORAM. Two polyethylene storage tanks each with a 550 L capacity are used to supply the system with distilled water, and the brine solution (for fouling experiments). One of the tanks has a mixer mounted on the frame. The mixer was used to initially stir the solution 58 Regenerative Heat Exchanger Preheater Preheater Water Water Line Conductivity Meter TEST SECTION Temperature Pressure Data Legend t\f}p- Overpressure ' Relief Valve Normally Open Valve N Normally Closed Valve NI Check Valve E l Back Pressure Regulator Figure 4.1: The UBC/NORAM SCWO facility 59 (during preparation) in the tank and was not used during the experiments. The outlet from the tank passes through a filter before reaching the inlet of the high pressure pump. The feed is pumped into the system at an pressure of 25 MPa by a high pressure, triplex positive displacement metering pump (GIANT P57). The pumping action of the cylinders can create some fluctuations in flow, so a pulsation damper (Hydrodynamics Flowguard DS-10-NBR-A- V2" NPT) was installed in direct line with the pump to suppresses these flow variations. The pump produces flow rates from 0.6 L/min to 2.2 L/min, and the maximum outlet pressure is 45 MPa. The rpm of the pump motor is controlled by a Variable Frequency Drive (VFD, Reliance Electric ISU21002). The system fluid first passes through a regenerative heat exchanger. This is a counter flow, tube-in-shell-type heat exchanger with 1.27 cm Schedule 80 pipe (SS 347) for the shell side. The cold process fluid flows through the tube side of the heat exchanger and the hot fluid flows through the shell side. After the heat exchanger two separately controlled preheaters are used to heat the fluid to the desired conditions for the test section. The preheaters are electrically heated by running AC current through the tube walls, which can be set at specified power values for experiments. Power is supplied by the silicon controlled rectifier (SCR) Panel directed through two step-down transformers (240/24 VAC, Hammond Manufacturing) for each preheater (figure 4.2). Each pair of transformers is wired in series in input and parallel in output. The transformers are attached to the preheater by 2.5 cm thick copper cables that lead to barrel connectors which are attached to stainless steel rods (SS 304). The steel rods are silver-soldered onto the tube itself. The high (max. 24 VAC) voltage connections are made at the middle of each preheater, and the ground connectors are at the ends, reducing the possibility of any ground loops in the system. The wiring arrangement also provides a balanced load to each half of the preheaters. Every transformer is capable of delivering 24 volts at 450 amps. The first preheater power is controlled manually from the SCR panel. The second preheater is equipped with feedback temperature control, but was kept on manual for all experiments. 60 Preheater One Preheater Two Test Section Parallel Series 240 ground 240 SCR Figure 4.2: Electrical heating schematic for the preheaters and test section. Heated Sections Union 1 Union 2 Union 4 Union 5 Barrel Connectors Figure 4.3: The test section of the SCWO system 61 The majority of the experiments were performed by extracting data from the test section. It is composed of two short (0.30 m) entrance and exit lengths, and two longer middle sections (1.52 m each) which are electrically heated in the same manner as the preheaters (figure 4.3). The sections are separated by five union fittings for possible disassembly and cleaning. After the test section, the process fluid flows through the shell side of the regenerative heat exchanger, and then through a process cooler, which takes the bulk temperature down below 50 °C. A back pressure regulator (Tescom #54-2162T24S) drops the pressure to just above atmospheric, and the flow is directed to the drain. All heated sections are insulated in 15.2 cm x 15.2 cm boxes of ceramic board (Kaowool). The thickness of insulation allows approximately a 0.151 kW/m power loss for a tube surface temperature of 380 °C (see section 5.2.1). A hazard and operability study (HAZGP) was completed for the SGWO system, with NORAM Engineering and Constructors Ltd. The purpose of the study was to examine all of the possible safety design issues relevant to the operation of the SCWO facility, and implement the changes that were recommended. Due to the nature of the experiments and complexity of the SCWO system, many safety features were incorporated into the final design. One of the main problems that could occur in the system is 'plugging' due to salt deposition. To prevent over-pressurization there are three pressure relief valves in the system, which can each relieve full pump flow rate at an over pressure of 29 MPa. Temperature is also monitored with four high temperature alarms, one at the outlet of each preheater, the test section and process cooler. These alarm set points are adjusted manually and shut off the power to the heaters when tripped. Additionally there are six surface temperature thermocouples at various locations that are connected to a six point display for visual monitoring of the system temperature. All of the temperature alarms and the temperature display are located on Control Panel Two, adjacent and attached to the SCR Control Panel. There is also a flow switch which will shut off power to the heaters for zero flow rate. For mechanical failures which might result in high temperature spray, the system is enclosed with 18 gauge steel sheet. 62 The SCWO User's Guide describes safety procedures in more detail, and all users must be "examined" by a qualified operator before using the pilot plant. 4.2 Instrumentation 4.2.1 Temperature Measurements Throughout the SCWO system, temperature measurements were used for safety issues as well as for experimental purposes. The temperature probes used for alarms were all Inconel sheathed, ungrounded probes, and were clamped onto the tube with steel straps. All experimental thermocouples used were K-type Chromel-Alumel with twisted shielded (for magnetic and electrical field protection) extension wire. The five union fittings in the test section have thermocouple ports in which Inconel sheathed and ungrounded thermocouples probes (B1..B5) were inserted to develop bulk temperature profiles. Twenty top, and nine bottom surface temperature thermocouples (S1..S20 and SB1..SB9 respectively) were also attached at various locations (figure 4.4) along the two middle sections. Due to the limited number of channels available on the data acquisition board, only 3 bulk and 16 surface thermocouples were used in all salt deposition experiments. Table A. 1 (Appendix A) contains the axial location of each thermocouple. It is important to note B . 2 SI etc. S10 B , 3 Sll S20 B , 4 Union 2 SB1 SB9 Union 3 Union 4 Figure 4.4: Position of the bulk and surface thermocouples on the test section 63 that the axial distance only refers to the heated length along the test section. The length between the two cable clamps adjacent to Union 3 (figure 4.3) was unheated, and was considered isothermal for modelling and experiments. The surface thermocouples were all attached by spot welding the two wires to the tube surface (figure 4.5). This arrangement uses the surface between the two wires as the junction for the thermocouple. Additionally, ceramic insulating rods were used to keep the wires isolated until they become encased by the high temperature ceramic fibre overbraid. It was important that the two spot welds were at the same axial position on the tube, so that the varying potential along the tube (due to the heating method) would not effect the accuracy. Before experimentation, a thermocouple was spot welded with the leads separated by an axial distance of 4 mm. Temperatures were recorded with the modified thermocouple and compared to the adjacent thermocouples. There was no noticeable effect in the accuracy of the measurement due to the axial distance (4 mm) between the spot welded wires. Since all other spot welds had a difference in axial distance of < 1 mm, it was assumed that the varying potential was negligible. The overall accuracy of the spot welded thermocouples is discussed in section 5.2.2. Spot Welds Overbraid Ceramic Rod Tube Top View Side View Figure 4.5: Spot welded attachment of surface thermocouples 64 4.2.2 Pressure Measurements Two differential pressure (Validyne DP303) cells, connected to pressure taps in the heated part of the test section, (figure 4.6) monitor the pressure drop up to 55 kPa (each) and output a 0 - 10 volt signal. There is a bypass line with a needle valve for each DP cell which is normally closed during operation. The bypass lines are opened to allow flow through the pressure taps for cleaning, and to protect the cells from any large pressure drops during start up. An absolute pressure transducer (Validyne Model P2) was also connected to the DP cell arrangement and was used to monitor the pressure fluctuations of the system. Union 2 Union 3 Union 4 Bypass Valve Bypass Valve Figure 4.6: Differential (DP) and absolute (P) pressure cells in the test section The DP cells were calibrated with a hand pump (Omega, PCL-2HP) and portable manometer (Omega, PCL-200) up to the full scale reading of 55 kPa. A linear fit was performed on the calibration data for each DP cell. The resulting two equations were: DP 427 AP = 0.70092 + 5.99304 (Vout) (4.1) 65 DP 429 AP = 1.68013 + 5.9042 (vovA) (4.2) where AP is the differential pressure drop [kPa] Vovt is the voltage reading [V] DP 427 is the first transducer in the test section DP 429 is the second transducer in the test section They have a rated error of 0.5% of full scale or .275 kPa. However, during operation of the test section, much larger pressure fluctuations (possibly resulting from the pump pulsation) were observed. These pressure variations were reduced at critical and supercritical temperatures. The error associated with the differential pressure fluctuations is discussed in section 5.5.5. The absolute pressure transducer outputs a 10 volt signal for a full scale reading of 34.5 MPa. Though the absolute pressure transducer was not calibrated, the visual readings of the pressure gauges during the experiments when compared to the absolute pressure data indicated an accuracy of + 0.5 MPa. 4.2.3 Power Measurements The RMS voltage (before the secondary transformers) supplied to each heated section (two preheaters, test section), is displayed on digital voltmeters on the SCR control panel. The voltage readings were only used as a qualitative indication of the heat flux applied to each section and so the accuracy was not important. The actual heat flux applied to the test section was calculated from the inlet and outlet bulk fluid enthalpies (see section 5.2.2). 66 4.2.4 Fluid Conductivity Measurements An on-line electrical conductivity meter (Omega CDH-287-KIT) was inserted after the back pressure regulator for real-time effluent conductivity measurements (figure 4.7). It was connected to the data acquisition board with an output signal of 100 mV. The rated accuracy is ± 0.3 % of full scale. The conductivity is a function of salt concentration, and calibrations were performed before experiments. The conductivity meter was calibrated by preparing nine sodium sulphate solutions ranging from 10"5 to 1 wt% and recording the conductivity of each solution. Several conductivity measurements were taken at each concentration and averaged. The conductivity meter was very consistent between measurements. The results were plotted on a log-log graph (figure 4.8) and a curve fit was calculated. The following equation relating concentration of sodium sulphate to conductivity was determined: (4.3) Conductivity Probe Fluid Flow T-Fitting Figure 4.7: Installation of the conductivity meter probe 67 Background 1.25 u.S/cm Temperature 28 deg. C ~* i I I 11 n i ) — i 111 u i i | i 111 nm i 1111 n i j — i 111 u n ) — i 11 | i 111 i u i | 1E-5 1E^ 1E-3 0.01 0.1 1 10 Concentration [wt%] Figure 4.8: Calibration of the Conductivity Meter where a is the electrical conductivity [ u.S/cm] C is the concentration of the salt solution [wt%] 4 . 3 Data Acquisition All temperature and pressure measurements were fed into a high-speed isolated data acquisition instrument (Omega MultiScan / 1200, figure 4.9). It provides channel-to-channel isolation which was needed due to the electrical potential on some areas of the test section (created by the method of direct electrical heating). There are 24 channels available, and 19 were used for temperature, 3 for pressure and 1 for conductivity. The MultiScan board was connected by RS232 cable to a personal computer which stored all of the sampled data. Tempview version 4.14 was the data acquisition program that interfaced the MultiScan/1200 board. It has a rated temperature accuracy for K-Type thermocouples of ± 0.6 °C. The Multiscan/1200 board samples data from each channel at 1.92 kHz, or once every 520.83 u.s. Tempview was configured to average 256 measurements for each of the 23 channels, which required a scan-time of 3.21 s. Therefore a sample interval of 5 seconds was chosen, which was greater than the minimum required scan-time. The signal averaging was done to eliminate noise from the silicon controlled rectifiers (SCRs) in the Control Panel. Tempview visually displayed all 23 channels being sampled, enabling the system to be monitored closely. For each experimental run the 23 channels of data were written to a text file every sample interval until the end of the fouling time. 69 Test Section 19 Temperature Measurements 3 Pressure Measurements 1 Conductivity Measurement of System Effluent Omega OMB-Multi Scan 1200 High Speed Isolated Measurement System 386 PC with Tempview4.14 Data Acquisition Software Figure 4.9: Data Acquisition System for the SCWO Facility 70 J 5. Experimental Procedure and Analysis The following chapter contains the procedure used for the salt deposition studies. The SCWO system was initially tested by completing some clean tube heat transfer measurements looking at heat loss and thermocouple accuracy for the test section. Then Na2S0 4 solubility experiments were completed with two different procedures, focusing on the critical to supercritical temperature region. The solubility studies formed the foundation for the more complex salt deposition experiments which examined the different salt deposition layers formed under specific test section conditions. 5.1 Operation of the SCWO System Operating the SCWO system was complex and potentially hazardous if the proper precautions were not taken. All of the experiments involved the same start-up procedure to facilitate safety and accurate experimental data. The data acquisition board was turned on one hour before experiments for proper 'warm up' time. Once the power was supplied to the SCR Panel, and Control Panel Two, the pump was turned on. The SCWO system always used distilled water for heat-up and cool-down. This was to prevent any scaling from impurities that might exist in common tap water. The bypass valves on the differential pressure cell arrangement were opened to allow flow through the pressure taps. The system was purged with cold water until the conductivity meter indicated that any salt left from the previous experiments had been cleaned out and the effluent was only distilled water (reading 1-2 u,S/cm). When the system had been initially purged of all accumulated deposits, the bypass valves were then closed and the system was pressurized to 25 MPa with the back pressure regulator (the system pressure was kept at 25 MPa whenever the process fluid was above 50 °C, to avoid boiling of the water, which might create local hot spots). During the experiments the back pressure regulator had to be regularly adjusted, especially at lower flow rates (0.65 kg/min), since it sometimes fluctuated as much as 1.4 MPa. 71 Once the system was pressurized, the spray shields were raised and secured. The _ power to the secondary transformers was activated and the process fluid was slowly heated. At this point according to the desired experimental conditions, the power was set, and the salt solution concentration was chosen. All data were accumulated and stored in a user-defined data file by activating the Tempview 4.14 software. Once the experiments were completed, the power to the heaters were shut off and the process fluid was switched back to distilled water for cool down. When the highest temperature in the system was 50 °C the back pressure regulator was decreased to atmospheric pressure. The pump was then stopped when the effluent conductivity indicated pure distilled water again, and the main power was then shut off. 5.2 Pure Water Heat Transfer Measurements 5.2.1 Heat Losses in the Test Section Though the test section insulation arrangement was planned to reduce heat losses, it was important to estimate the heat transfer through the insulation for a given outside surface temperature of the tube. Experiments were performed by heating distilled water with the two preheaters to a desired bulk inlet temperature for the test section. The test section however, was kept unheated, and the outlet bulk temperature was recorded. The experiments originally were performed at high mass flow rates (2.2 kg/min), but produced inlet to outlet temperature differences which were too small to accurately measure (heat losses calculated in some cases were negative). The actual heat loss should be independent of mass flow and only a function of the thermal conductivity of the insulation and temperature difference from the tube to the air. Therefore experiments were performed at lower mass flow rates (0.633 kg/min) to create a larger inlet to outlet bulk temperature difference. From the measured temperatures and absolute pressure the thermodynamics program EQTEST.f was used to obtain inlet HM and outlet 7f0ut enthalpies [kJ/kg]. The 72 heat flux (loss) into the fluid was determined by performing an energy balance with enthalpies: m(Hmi-H^) 2.946 where 2.946 is the length [m] of the test section. An average outside surface temperature was calculated using the thermocouple measurements. The results are contained in table 5.1. Table 5.1: Results of heat loss experiments Mass Flow [kg/min] Inlet Bulk T [°C] Average Surface T [°C] Heat Loss [kW/m] 0.633 155.48 148.45 0.043 0.633 344.25 334.41 0.114 To verify our assumption that heat loss was independent of mass flow, the heat loss values for the low mass flow runs were used to predict outlet bulk temperatures for high mass flow runs. Three experiments used a mass flow of 2.23 kg/min, and average surface temperatures were calculated for each. Heat losses corresponding to these average surface temperatures were interpolated from the data in table 5.1. Using these heat losses and the inlet temperature (enthalpy), the outlet bulk temperature was estimated with an energy balance (to detenriine the decrease in enthalpy) and was compared to the actual measured outlet bulk temperature. The results are contained in table 5.2. The differences between predicted bulk and measured bulk temperatures were all less than 1.3 °C (which was less than the recorded drift of the bulk temperatures (2 °C) over the experimental run). This implies that within system temperature fluctuations, the low mass flow rate heat losses can be applied to the high mass flow case. However it was 73 later decided that the heat loss information would not be used in calculation of the heat flux for the test section. It was considered more accurate to use inlet and outlet enthalpies to calculate the amount of heat the fluid had absorbed (see section 5.2.2) than rely on the power measurements (SCR Control Panel) and heat loss information. Table 5.2: Results for extrapolation of low mass flow, heat loss data to the high mass flow condition Mass Flow Avg. Surf. Heat Loss Predicted Measured Difference [kg/min T[°C] Interpolated Outlet Bulk T Outlet Bulk T [°C] [kW/m] r°ci r°ci 2.23 209.94 0.094 206.2 207.5 1.3 2.23 265.83 0.114 268.5 269.4 0.9 2.23 380.19 0.151 384.6 385.0 0.4 5.2.2 Testing the Thermocouple Measurement Accuracy Heat transfer experiments with distilled water in a heated test section were performed to compare the thermocouple measurements with predicted outside surface temperatures from the program SCHeat.f. The mass flow rate was kept constant at approximately 2.2 kg/min and in particular two temperature ranges (corresponding to sub-critical and near critical temperatures) were used. The heat flux was calculated with equation 5.1, and SCHeat.f. was used to generate temperature profiles which were compared to the data (figures 5.1 and 5.2). In both cases the model predictions are very close to the experimental data. Even with the large property variations in the critical region, the thermocouple measurements were within 1 °C of the model. Bottom surface thermocouples were also included to estimate any radial temperature gradients (due to buoyancy) and appear to be consistent (only in one case 2 °C higher) with the top mounted thermocouples (see Appendix E). The second bulk temperature thermocouple was consistently lower (by 3 °C) and cannot be explained. It should be noted that if a temperature profile was taken at an earlier time 74 Figure 5.1: Comparison of experimental and model temperature profiles for distilled water in a heated test section at 25 MPa and sub-critical temperatures. Figure 5.2: Comparison of experimental and model generated temperature profiles in a heated test section at 25 MPa and near critical temperatures. 75 experimental data for figure 5.1, the thermocouple readings appeared scattered and did not agree with the model predictions. However, at some point during the experiment, all of the temperatures changed producing the results displayed in figure 5.1. It was thought that the data acquisition board had not had enough time to warm up (manual suggests 1 hour), and that this warm up period was completed mid-run, which led to the increase in thermocouple accuracy. Another difficulty with the thermocouple arrangement, was that the test section underwent axial thermal expansion of 3-4 cm during heating. With the insulation clamped onto the tube, the thermocouples and spot weld attachments were placed under stress. This required periodic checks to ensure that the junctions for the thermocouples were occurring on the tube surface and not further away due to crossed wires. In some of the salt deposition experiments that followed, this process affected two thermocouple measurements. 5.3 Sodium Sulphate Solubility Experiments 5.3.1 Procedure A series of solubility experiments were performed from sub-critical to supercritical temperatures at 25 MPa. The basic concept involved keeping the test section isothermal, so that the entire length would be at one solubility hmit (figure 5.3). It was assumed that a solution flowing through the test section would deposit all salt above the solubility hmit on the tube walls. Therefore, the concentration of the effluent solution was at the solubility hmit corresponding to the temperature of the test section. In this way a temperature-solubility curve was developed. The first step in the experiments was to prepare a solution of sodium sulphate and water in the cylindrical storage tank. The mass of sodium sulphate mM\t [kg] needed for a given concentration solution was calculated using the following equation: 76 where ma^d is the mass of water [kg]. The mass of Na2SC«4 was measured with a digital table-top scale, and dissolved into a 4 litre beaker with a stirrer. If over 180 grams of salt was needed, the previous procedure was repeated several times. Then the solution was added to the storage tank (550 L) and diluted with the amount of distilled water indicated by fflfluid. The stirrer on the storage tank was then turned on for a minute to increase the mixing process. Finally the conductivity of both the distilled tank and the brine solution was measured and recorded. The experiments were run at the pump's lowest flow rate of 0.65 kg/min, and also at a higher flow rate of 1.20 kg/min. This was to test the assumption that the test section provided enough residence time so that all salt above the solubility limit could deposit on Isothermal Test Section Enters at an Initial Deposits Salt Above Exits at the Concentration Above the Solubility Solubility Limit Solubility Limit Figure 5.3: Experimental methodfor salt solubility experiments. 77 the walls. If the assumption was false, the higher flow rate should produce effluent concentrations that are consistently higher (transported salt re-dissolves after test section as the fluid cools) than the lower flow rate for the same conditions. The test section was kept as isothermal as possible (bulk temperature from inlet to outlet was approximately 1 °C). When the temperature profile reached a steady state, the influent was switched to the brine solution. The test section temperature profile and effluent conductivity were measured and recorded. When the conductivity reading reached a steady value, it was recorded as the solubility limit for the test section temperature2. There was concern that the solubility measurements might be affected by deposition kinetics, so an alternate procedure was attempted. This method incorporated salt that had previously been deposited in the test section as a 'salt bed'. Once a significant amount of salt had been deposited in the test section, the influent was switched to pure distilled water. With the test section kept isothermal, it was assumed that the pure water dissolved enough salt to become saturated by the time it exited the 'salt bed'. Therefore the concentration of the effluent was the solubility hmit. During the experiments it became apparent that the 'salt-bed' method was questionable. In creating the salt bed, some fouling occurred in the preheaters. When the pure water was sent through the system, it dissolved the salt in the preheaters first (which were at lower temperatures than the test section) and may have been above the solubility limit (of the isothermal test section) when it reached the test section. If so, the process fluid was a salt solution depositing salt above the solubility limit in the test section and not a pure water feed re-dissolving salt from a salt-bed. The uncertainties in the 'salt-bed' method were large enough so that the procedure did not distinguish itself from the other solubility experiments. 2 When the conductivity meter changed its range, the output signal remained from 0 - 100 mV. By examining the data file alone, the order of magnitude of the conductivity measurement was uncertain. Visual readings of the meter were taken during experiments to determine the order of magnitude of the conductivity. 78 5.3.2 Producing the Solubility Curve Twenty-two different solubility points were taken from 374 °C to 505 °C, using two different flow rates (0.66 L/min and 1.2 L/min). All of the data were analysed using the same technique. Before the data could be analysed, it was important to determine the residence time for each flow rate from the outlet of the test section to the conductivity meter. The total volume of the SCWO system (from the inlet to the pressure regulator, neglecting the filter volume) is approximately 2.3 L. A flow rate of 1.22 L/min produces a residence time of 113 seconds. During the experimentation, the residence time appeared to be slightly longer at 130 seconds. For the lower flow rate of 0.66 L/min, the residence time was significantly longer at 180-240 seconds. The total residence time was reduced by 50% to estimate the time from the outlet of the test section to the conductivity meter. The data file was imported into a spreadsheet and visually scanned for steady state conductivity measurements of the effluent. Ten to fifteen points were averaged for a conductivity reading and incorporating the correction for residence time, ten to fifteen points were averaged for a bulk temperature reading for the test section. The conductivity readings were then corrected for the background of the distilled water, and converted into concentration values using equation 4.3. 5.3.3 Analysis and Comparison of Solubility Data The results for all solubility experiments are displayed in figure 5.4. Data from previous work has also been included for comparison. The solubility curve has a distinct shape, with a sharp decrease in solubility at the pseudo-critical point (385 °C and 25 MPa), dropping three orders of magnitude over 5 °C. The pseudo-critical temperature is defined as the temperature at a supercritical pressure, that has the maximum compressibility for the fluid. After 390 °C the curve shallows dramatically (decreasing one order of magnitude over 100 °C). The increase in scattering at 500 °C was expected due to the conductivity measurements reaching the resolution of the conductivity meter. 79 510 490 --470 --FT 450 --ire[( 430 -mperati 410 --390 --<o E- 370 -350 330 310 l.E-07 l.E-05 l.E-03 l.E-01 l.E+01 Concentration [wt%] l.E+03 o Chan et. al (1994) A Interpolation of Martynova (1973) o This Study 0.65 kg/min (1997) e This Study Salt Bed (1997) X Morey and Hesselgesser (1951) + 1 C Error - Solubility Eq. (Chan et aL, 1994) Armellini and Tester (1992) This Study 1.2 kg/min (1997) Ravich and Borovaya (1964) • Pseudocritical Temperature -1 CError Figure 5.4: Summary of data for solubility of sodium sulphate in water at 25 MPa. 80 The variation in mass flow had little effect on the solubility measurements. If a significant amount of transport was occurring in the test section, the higher mass flow should consistently produce higher concentrations. But in two cases the lower mass flow produced higher concentrations. Therefore the mass flow ranges in the experiment did not effect the solubility experiments. However, much lower mass flow rates could provide more insight into the validity of the assumption. The only previous comprehensive measurements of the solubility of sodium sulphate were performed at sub-critical temperatures. This was probably due to the method of the experiments, which used an autoclave to measure the pressure drop associated with the dissolution of salt in pure water (see section 2.5.1). Both Chan et al. (1994) and Armellini and Tester (1993) each have one data point above the critical region, but Chan et al.'s concentrations are one to two orders of magnitude (concentration) lower than ours, so it appears that there is a large discrepancy in the data. Chan et al. also used a flow type arrangement for their experiments, but at much lower flow rates (0.036 kg/min). The discrepancy would be consistent with the idea that at higher mass flow rates there is some transport and re-dissolution of salt. But the consistency of our data both below the pseudo-critical temperature (with Martynova, and Ravich and Borovaya, 1964) and Armellini and Tester's (1993) point at 500 °C appear to favour the accuracy of our measurements. Additionally these solubility points were determined with different experimental methods which strengthens the accuracy. Morey and Hesselgesser's (1951) solubility at 500 °C was two orders of magnitude greater than our data. However, the solubility point was determined for this study by interpolating between two data points at 13.3 and 66.6 MPa. It is known that pressure affects the solubility, especially near the critical point, and since our pressure was near critical (25 MPa) a linear interpolation was not very accurate. 5.3.4 Curve Fitting the Sodium Sulphate in Water Solubility Limit In order to use solubility measurements in the models, a curve fit was completed. The data were fitted in three separate temperature ranges: 81 -3.49612 In T-337.70602 49.11281 r - J ,n(232.3458-0.605186 T) -^sat - ] J U 2.2 {T-385.645) In [lOOO T12) 32.19 337.7 <T< 385.8 °C 385.8 <T<388.5 °C T> 388.5 °C (5.3) where T is the temperature in degrees Celsius. All three sections were graphed with the data in figure 5.5. It was important to match the start and end points of each section, though it was too difficult to keep the slopes continuous from one section to another. The slight deviation from the data above 450 °C, was not that significant for the deposition model, considering that the concentrations are so low (< 10"4 wt%) in this region. 5.3.5 Evaluating the Error of the Solubility Data An important error to evaluate in the solubility experiments was the assumption that the solution had sufficient residence time in the test section to deposit all of the salt above the solubility limit. To test the assumption some results from the salt deposition studies were used. In the salt deposition experiments (see section 5.4) the test section was not kept isothermal, but instead had a large temperature gradient (10-20 °C) along the length. Therefore the outlet bulk temperature dictated a solubility limit (using the solubility curve) which the solution only had a few centimetres of tube length to deposit (compared to the 3 m of length in the solubility experiments). Table 5.3 contains the bulk outlet temperatures for the salt deposition experiments and the corresponding solubility limits. It also contains the actual measured effluent concentrations and the percentage difference. 82 1.0E+02 1 — . l.OE+01 % l.OE+00 g l.OE-01 --& 1.0E-02 -C | l.OE-03 o ^ 1.0E-04 Pressure 25 MPa l.OE-05 330 380 430 480 Temperature [C] 530 Curve Fit Data Figure 5.5: Curve fit to the solubility data for sodium sulphate in water at 25 MPa. 83 Table 5.3: Salt deposition effluent concentrations used as an error estimate on the solubility experiments. Outlet Bulk Temp. Solubility Measured Effluent Percentage Difference [°C] [wt%l Concentration [wt%] [%] 383.6 0.23699 0.15759 -12.2 384.2 0.191577 0.19360 0.3 383.6 0.23699 0.21565 -3.6 383.8 0.22178 0.30224 13.5 385.7 0.08057 0.17205 15.4 387.6 0.00597 0.03677 7.6 385.7 0.08057 0.09066 2.5 385.8 0.07329 0.07860 0.5 385.6 0.08786 0.06311 -2.3 385.7 0.08057 0.05633 -12.4 388.4 0.00196 0.03687 17.9 The largest percentage difference was 17.9 % and was considered an over-estimate of the error on the actual solubility experiments. The reasoning was that the outlet temperatures in the salt deposition experiments had a much shorter length (factor of one hundred less) to deposit everything above the solubility limit. Regardless, even if there was an average concentration error of 8 %, it would not be noticeable on the log scale solubility graph (figure 5.4). It is interesting to note that in some of the runs, the effluent concentration was actually less than the solubility limit at outlet bulk temperature. This indicated that salt deposition may be influenced by the wall temperature as well, and this idea will be explored in the analysis of the salt deposition experiments. Another error that was considered was the accuracy of the bulk temperature measurements. This error was important for validating the statement that the sharp decrease in solubility actually starts at the pseudo-critical temperature. The 'isothermal' test section had inlet to outlet bulk temperatures that differed from 0.5 to 1.5 °C depending on the experiment. Within this temperature error, the solubility curve definitely starts it's rapid decrease at the pseudo-critical temperature. 84 5.4 Sodium Sulphate Deposition Experiments The purpose of the salt deposition experiments was to foul the test section with sodium sulphate and produce a measurable indication of the thickness of the salt deposit layer. Fourteen experiments were completed, and eleven were analysed. For six of the runs, mass balances were used to determine a thermal conductivity for sodium sulphate at the experimental temperatures. The two methods of monitoring the deposition profile were through outside wall temperature fluctuations, and differential pressure drop. The fouled tube temperature measurements were used to estimate salt layer thicknesses considering conduction in the salt layer. The salt profiles were compared to several salt deposition models. Finally the pressure drop measurements were compared to the model predictions. 5.4.1 Procedure The salt solution was prepared is the same manner as in the solubility experiments. Once the system was heated up to steady state with distilled water the influent was switched to the salt solution and the temperature, effluent concentration, and differential pressure measurements were visually monitored and stored by computer. The differential pressure transducers had a maximum reading of 55 kPa each. All fouling experiments were run until the measured differential pressure was close to this value, at which point the heaters were turned off. The influent was then switched back to distilled water to flush out the salt deposits and cool down the system. The following table contains an outline of the 14 experimental runs that were completed. All relevant information (including power settings, pump motor speed, etc.) were also recorded in the SCWO log book. Runs 6,1, and 8 were originally completed to examine the reproducibility of runs 4, 5, and 6. For reasons that will be explained later in this chapter, they were not analysed in full and will not be included in any of the remaining discussion. 85 Table 5.4: Salt deposition experiments summary. Run No./ Cone. Mass Flow Temp Range Heat Flux Time Mass Date [wt%] [kg/min] [°C] [kW/m] [s] Balance 1./July 4 0.652 1.21 373-384 2.07 375 No 2. 0.652 0.66 375-384 0.80 710 No 3. / July 24 0.595 1.20 373-384 2.04 475 No 4. 0.595 2.22 372-384 2.68 203 No 5. 0.595 0.68 370-386 1.17 966 No 6. / July 25 0.580 1.21 Not Analysed NA 475 No 7. 0.580 2.21 Not Analysed NA 210 No 8. 0.580 0.64 Not Analysed NA 966 No 9./Aug 11 0.408 0.62 371-388 1.52 620 Yes 10. / Aug 12 0.408 1.23 363-386 2.98 510 Yes 11./Aug 22 1.066 2.16 365-386 5.58 80 Yes 12. 1.066 0.70 364-386 1.81 478 Yes 13. 0.195 2.18 363-386 5.73 342 Yes 14. 0.195 0.63 365-388 1.66 1890 Yes For some of the runs (9 - 14), two surface thermocouples (SI7 and SI9) were producing erratic readings that were 60 - 80 °C lower than expected. It was noticed that during some experimental runs, the temperature reading varied from 400 to 320 °C between one sampling period. If the temperature, when compared to the adjacent thermocouples, was much lower, it was assumed that a junction had been formed further away from the tube surface (a lower temperature reading) due to the thermal expansion of the test section placing stress on the thermocouple wires (see section 5.2). Therefore these measurements were ignored. 5.4.2 Mass Balance On several of the salt deposition experiments a mass balance was completed to check if there was any salt deposits being accumulated permanently in the apparatus (see table 5.5). The mass flow rate was measured in all runs by placing a graduated cylinder at 86 Table 5.5: The results of the mass balance for the last six salt deposition runs. A comparison between the salt delivered to the system and the salt collected at the outlet. Run Cone Mass Flow Delivery Total Delivered Total Percent No. [wt%] [kg/min] Time Period [g] Collected Difference rsi rg] r%i 9 0.408 0.62 620 26 21 -19.2 10 0.408 1.23 729 62 51 -17.7 11 1.066 2.16 80 31 54 74.2 12 1.066 0.70 478 61 75 23.0 13 0.195 2.18 342 24 28 16.7 14 0.195 0.63 1890 39 42 7.7 the outlet of the system and timing the volumetric flow. For the mass balances the effluent was collected in two separated 20 litre distilled water jugs. The first one was used for collection during the salt deposition period when the sodium sulphate solution was on-line. Collection started when the effluent concentration started to increase rapidly (indicating the first amount of salt solution had passed through the system). The second jug was used to collect the effluent during the clean-out period when the distilled water (for run 10 the salt solution was used for clean-out) was on-line. Collection with the second jug started when the effluent concentration increased again (as soon as the heaters were turned off, the salt layer re-dissolves into the process fluid increasing the concentration). The clean-out period was not stopped until the effluent conductivity measurement was approximately at distilled water levels. The period that the salt solution tank was open was timed to determine the amount of salt delivered to the system. The collection times for both sample jugs were also recorded, but should not be important in determining the total salt collected. The following table contains the results from the six mass balances completed during the salt deposition experiments. The total mass delivered was calculated with the time that the salt solution tank was open, the mass flow rate, and the concentration: 87 /"salt = " W r ' \ 1 Q Q _ C ) ( 5 4 ) where /wwater is the mass flow of water [kg/s]. For the total mass collected, the conductivity and volume of each jug was measured and equation 5.4 was used substituting 'Fpb'for the 'm f term. The percentage difference Am was calculated with: ^ =/"collect-/"salt x l Q Q O / o ( ^ /"salt where moiled is the mass of salt collected in both sample jugs [kg]. In examining the results there was a wide range of discrepancies in the mass balance. Run 11 had the highest percent deviation at 74 %, and run 14 the lowest at 8 %. From these results it appeared that the higher concentration runs, with shorter fouling times, had the greatest error in the mass balance. Conversely, run 14 was the longest run with the lowest concentration and had the best result. Therefore the error in the mass balances was largely dependent on the fouling time (the time the salt tank was on-line). It could be that the shorter fouling times were similar in length to the time scales of the transients associated with the system (residence time, mixing in the regenerative heat exchanger and differential pressure cell plumbing). The transients were most noticeable in the variations in concentrations at the effluent. The concentration profile with respect to time, during one experimental run was as follows: 1) Distilled water levels for start up (1-2 u.S/cm) 2) Rapid increase (orders of magnitude) as salt solution first passes through the system (collection jug #1 inserted) 3) The concentration then slowly decreases (same order of magnitude) 88 4) When the heaters are turned off and pure water is sent through, there is an initial spike (in concentration) as the first re-dissolved salts exit the system (several orders of magnitude above stage 2) (collection jug #2 inserted). 5) Fairly rapid decrease back to distilled water levels (time: 20-30 minutes). Stages 2 and 4 had the largest variations in concentrations and therefore the start and stop points at which the two collection jugs were inserted into the effluent would be the source of the largest errors in the mass balance. These errors were difficult to estimate without further more detailed experiments. Other errors in calculating (volume and conductivity measurements) the mass delivered and collected from the samples were small (~ ± 1%). The results from the mass balance experiments indicate that the SCWO system transient characteristics should be studied in more detail for more accurate design of experiments. Sections such as the tube-in-shell regenerative heat exchanger with an annulus, may require long periods of time to purge the initial process fluid (switching from distilled water to salt solution and vice versa). 5.4.3 Inferences from Temperature Measurement There were 11 salt deposition experiments that were analysed. Runs 6, 7 and 8 were compared to runs 3, 4 and 5 to see if the experiments were reproducible (figure 5.6). The temperature profiles were very similar, and no further analysis was completed with runs 6, 7 and 8. Axial temperature profiles were available for every sample time during the total fouling time. Effluent conductivity, and differential and absolute pressure measurements were also available. Each of the salt deposition experiments was allowed to run until the pressure drop reached the maximum reading of the DP cells (55 kPa each), so many of the experiments had different fouling times. For reasonable and comparable salt thicknesses, it was decided that the total mass of salt delivered to the test section would be kept the same for each run. Run 13 delivered the lowest amount of salt (24 grams). All other runs delivered 89 1.25 1.20 H 115 H 1.10 1.05 + 1.00 A $ i n : ; A A o t • • ° © • © • • • • 0.0 0.5 1.0 1.5 2.0 Axial Distance [m] 2.5 3.0 Clean Tube © Run 3 A Run 4 D Run 5 • Run 6 A Run 7 • Run 8 Figure 5.6: Comparison of similar runs, to determine the reproducibility of the experiments Table 5.6: Summary of equal mass delivery calculations. Run No. Cone. Flow Rate Total Fouling Mass Delivered Fouling Time [wt%] [kg/min] Time [s] [kg] For 0.024 kg [s] 1 0.652 1.21 375 0.050 183 2 0.652 0.66 710 0.051 336 3 0.595 1.20 475 0.057 203 4 0.595 2.22 203 0.045 110 5 0.595 0.68 966 0.065 358 9 0.408 0.62 620 0.026 574 10 0.408 1.23 510 0.043 289 11 1.066 2.16 80 0.031 63 12 1.066 0.70 478 0.060 193 13 0.195 2.18 342 0.024 342 14 0.195 0.63 1890 0.039 1184 90 more salt than run 13, so a time period that delivered 24 grams of salt had to be determined for each run. To determine this fouling time, equation 5.4 was solved for t for each run, with 24 grams as the total salt delivered m^n to the test section (see table 5.6 column 6). The end of the total fouling period was defined as the sample in the data in which the heaters were turned off. The start time was obtained by subtracting the total fouling time (column 4 in table 5.6) from the end. Then the time for a mass delivery of 0.024 kg of salt (column 5 in table 5.6) was added to this start time to locate the sample interval for analysis. From the temperature profiles the bulk temperatures were analysed with the same method employed in the pure distilled water heat transfer experiments (see section 5.2.2). The computer program (SCHeat.f) was then used to generate salt deposition profiles (all four deposition models) for the eleven runs. In order to compare the results with the experimental data, the outside surface temperatures measured from the test section had to be converted to corresponding salt thicknesses. 5.4.4 Program Procedures for Comparing Predictions to Experimental Data Two procedures were implemented in the computer program (SCHeat.f) so that data from the experimental system could be compared to predictions of the program. The first was that a salt layer decreased the radial thermal conduction compared to a clean tube, which lead to an increase in outside wall temperature (with constant heat flux applied). The second was an assumption that the salt layer increased the roughness of the tube proportional to its thickness. This created an increased pressure drop along the length of a fouled tube. 91 5.4.4.1 Predicting the Outside Wall Temperature for a Fouled Tube As the salt layer increases in thickness, the inside and outside tube surface temperatures increase. The thermal conductivity of the salt layer was assumed to be equivalent to a network of stagnant water and salt columns in parallel. The overall thermal conductivity was calculated with the following equation: where kiiya is the thermal conductivity of the salt layer [W/m-K] k„\i is the thermal conductivity of the salt [W/m-K] To calculate the temperature through the salt layer, a one dimensional radial heat conduction equation was used: where r, is the radius from the centre of the tube to the salt layer [m]. T, is salt layer-fluid interface temperature, and is calculated by equation 2.4 in only the fouled section of the tube. With Tv calculated by equation 5.7, equation 3.4 was again used to calculate the outside wall temperature. Since the only data found for the thermal conductivity of sodium sulphate was a single measurement at room temperature (Dickerson, 1965), it was determined iteratively for near critical temperatures by the algorithm of figure 5.9. *layer ={l~<f) *salt+^* (5.6) (5.7) 92 A program was written to convert the measured outside surface temperatures to a salt layer thickness on the inside tube wall (written in FORTRAN-77 and called Salt.f). The procedure and equations for heat transfer used in Salt.f were exactly the same as SCHeat.f, but the axial step sizes zlz taken were equal to the thermocouple positions on the test section (table A.l). The program compared the outside surface temperature it calculated assuming no salt layer with the experimental value (figure 5.7). If the experimental value was larger it added a thin salt layer and recalculated the outside surface temperature (the decrease in fluid flow diameter was incorporated into all heat transfer calculations). The thermal conductivity of the salt was initially estimated with sodium chloride (4.2 kW/m) and was assumed constant over the entire layer. The salt layer thickness was gradually increased until the temperature difference Te(exp) - Te(model.) was less than 0.1 °C. This criterion is less than the accuracy of the thermocouples (1°C). Once all sixteen temperature data points were converted to salt thicknesses, the temperature and deposition profile were written to a data file. The salt layer thickness profiles were only as accurate as the estimation of the thermal conductivity of the salt. Since the properties of sodium chloride differ from sodium sulphate, Salt.f was modified so that a value for could be chosen, and then used to determine the salt layer thickness. The salt deposition profile was then integrated to determine a volume for the layer. The volume calculations approximated the salt layer as cylinders of zlz length with wall thickness j>Mit equal to the salt layer thickness and then added all cylinders to determine a total volume (figure 5.8). The volume can then be converted to a mass: 'layer all salt cylinders I (5.8) where m\iyet is the mass of salt calculated from the inferred salt layer [kg]. 93 Uses SCHeat.f to determine the outside surface temperature Tt (clean tube first iteration) Use equation 5.7 to calculate temperature increase through salt layer Create a thin salt layer with thermal conductivity Mayer (equation 5.6) using Malt for sodium chloride The salt layer also changes the diameter used in all calculations Figure 5.7: The algorithm for the program Salt.f which converts the outside surface temperature data to a salt layer thickness. 94 Cross Section of Tube H * One salt ^ y 'cylinder' Add all salt 'cylinders' of Az in length and ysa\i in wall thickness to determine total salt layer volume Figure 5.8: Calculation of the salt layer volume by approximating the layer as a series of 'cylinders' of length Az and wall thickness yfait. This process was completed for the six runs with mass balances. For purposes of the thermal conductivity calculations, the mass balances were assumed accurate. For each run, the thermal conductivity of the salt was varied (figure 5.9) until the mass calculated from the salt profile was within 0.5 grams of the amount the mass balance indicated was deposited m^ [kg] (this was determined by subtracting the mass collected at the effluent during fouling, from the mass delivered; the difference was assumed to be deposited in the test section). The results from all six runs were averaged (range of values 2.5-9.8 W/m-K) to estimate a thermal conductivity of 5.8 W/m-K for sodium sulphate. 95 Input Malt *" Algorithm from figure 5.7 used for all 16 temperature measurements Convert salt layer to mass deposited Figure 5.9: Algorithm used to determine the thermal conductivity of sodium sulphate. 96 5.4.4.2 Estimation of Increased Flow Resistance The exact dependence of pressure drop on salt thickness is not known, so in the absence of information on the nature of salt deposits, it was assumed that for fouled tubes, the roughness value was equal to the average thickness of salt deposit. This assumption approximated the shape of the salt layer as a series of peaks and valleys of an average height equal to the salt layer. The peaks and valleys increased the roughness of the tube, affecting the frictional losses. For thick layers it was thought that this would be an over-estimate. The increased roughness was not included in the heat transfer calculations. For flow in a tube, the pressure drop AP over a section was calculated with: AP = 8 f Az md d5p, n2 (5.9) and the Haaland (1983) equation for the friction factor / was used: 1.8 log, '6.9 s V J A 10 Re 3.7 dj (5.10) where e is the roughness factor of the clean tube and was 0.002 mm. Haaland's (1983) equation for the friction factor is a variation of the traditional Colebrook (1938) equation: / = 2.0 log 10 2.51 e {Re f1/2 3.7 d) ui\ -2 (5.11) 97 which combines the smooth wall and fully rough relations in an interpolation formula. For the purposes of the program, the Haaland (1983) formula was more efficient and varies less than 2 % (White, 1986) from Colebrook (1938), which was an acceptable error. For a tube with a fouled section, the assumption of tube roughness equal to the salt layer thickness was applied: *fe>ui = £+ysalt ( 5 1 2 ) where 6f0Ui is the new tube roughness [mm]. With equation 5.8, 5.9 and 5.11, the pressure drop over a fouled section was calculated. 5.5 Comparing the Experimental Salt Deposition Profiles with the Model Predictions As a review the four salt deposition models are: Model 1: 'Suspended Particles' which has molecular diffusion and nucleation, but no particle deposition; Model 2: 'No Nucleation' which has molecular diffusion and no nucleation; Model 3: 'Chan et al.' which has no mass transport limitations for dissolved salt above the solubility limit; and Model 4: 'Complete' which has molecular diffusion and particle deposition. The salt thickness profiles generated by SCHeat.f and experimental data converted by Salt.f, were plotted as a function of axial distance aiong the test section. Table 5.7 contains a summary of the results and a sample run (11) is displayed (figure 5.10). All graphs are contained in Appendix B (figures Bl to Bl 1). The first observation from examining the experimental salt deposition profiles was that runs 1-5 when compared to runs 9-14, had a salt deposit thickness on average 2-3 times less. To verify that this was not just an error in the program Salt.f, the original temperature data were examined, and the outside surface temperatures for runs 1-5 were 98 Table 5.7: Comparison between model predictions and experimental data. Run Cone. [wt%] Flow [kg/min] Model 1,2 and 4 Salt Layer Peak Location / Height [ml / [mm] Model 3 Salt Layer Peak Location / Height [m] / rmm] Experimental Salt Layer Peak Location / Height [m] / [mm] 1 0.652 1.21 0.8 0.6 1.0 1.1 1.55 0.2 2 0.652 0.66 0.8 0.5 0.8 0.9 1.02 0.1 3 0.595 1.20 1.0 0.5 1.1 1.1 1.90 0.3 4 0.595 2.22 1.7 0.5 1.5 1.0 2.41 0.3 5 0.595 0.68 1.3 0.8 1.2 1.7 1.90 0.4 9 0.408 0.62 0.9 1.2 12 2.8 1.90 2.2 10 0.408 1.23 1.5 1.0 1.7 2.3 2.28 1.3 11 1.066 2.16 0.6 0.9 0.8 2.3 1.41 1.3 12 1.066 0.70 0.7 0.9 0.8 2.4 , 1.02 1.2 13 0.195 2.18 1.6 1.2 2.4 2.2 2.55 1.5 14 0.195 0.63 1.2 1.6 1.8 Plugged 2.28 2.2 Run 11 2.5 T 0.0 0.5 1.0 1.5 2.0 2.5 3.0 Axial Distance [m] •B— Suspended Particles —e— No Nucleation —A— Chan et al. —X— Complete • E e^rimental Figure 5.10: Comparison of experimental and predicted salt deposition profiles for sodium sulphate in a heated tube at 25 MPa and near critical temperatures. 99 100 - 150 °C less. The only difference between the sets of runs was that the inlet bulk temperatures for runs 1-5 were approximately 370 - 373 °C and for runs 9-14 were approximately 365 °C (except for run 9). This led us to consider deposition in the preheaters. Due to heat loss in an unheated, insulated tube bend, between the last preheater and the test section, it is possible that the preheater wall temperature was significantly higher than the bulk temperature in the test section. Thus, the first salt might have been deposited in the preheater, rather than the test section. 5.5.1 Modelling the Salt Deposition in the Second Preheater Due to the lack of instrumentation on the preheater, the program SCHeat.f was needed to model the salt deposition (if any) that was occurring at the inner tube wall. To determine the inlet conditions of the preheater for SCHeat.f, an energy balance was performed starting at the inlet of the test section. The inlet bulk enthalpy for the test section was calculated with the bulk temperature and EQTEST.f. To determine the outlet of the preheater, the heat losses for the tube bend with insulation had to be estimated (except for runs 1 and 2, which had no insulation on the majority of the bend). Heat loss experiments were done for the test section (see section 5.2.1), with similar insulation characteristics. For an average surface temperature of 380 °C, a heat loss of 0.151 kW/m was calculated. This was used for the unheated section for a length of 1.10 m (tube bend and three short straight sections) and 0.54 m for runs 1 and 2. Also there was 0.15 m of uninsulated tube due to the method by which the blanket was wrapped around the tube bend and for the first two runs an uninsulated length of 0.71 m. Free convection heat transfer correlations (Holman, 1981) for vertical cylinders with isothermal surfaces give: Nu{=B(Gr{Prf)n (5.13) 100 where B and n are experimentally determined constants and depend on the product of the Grashof Gn and Prandtl Prf numbers evaluated at the film Tf temperature: 2 (5.14) where Tx is the ambient temperature of the air surrounding the tube bend (25 °C). The Grashof number is the ratio of buoyancy forces to viscous forces in a free-convection flow system: where g is gravitational acceleration (9.81 m/s2) B is the volumetric expansion coefficient, and for a perfect gas equals 1/T [1/K] z is the length of the uninsulated tube [m] all subscripts 'f' indicate the property is evaluated at the film temperature The Grashof and Prandtl numbers were calculated and used to evaluate equation 5.13 for the Nusselt number (heat transfer coefficient) using the constants B =0.59 and n = 0.25 (table 7-1, Holman, 1981). With the heat transfer coefficient the uninsulated (free-convective) heat losses were determined and with the calibrated insulated losses, the total was 0.710 kW for runs 1 and 2, and 0.209 kW for all other runs. Using these values the outlet enthalpy of the preheater for each run was calculated with: g&(Tw-Tx C"f I Pif (5.15) H, outPHl •loss (5.16) where // 0utPH2 is the bulk outlet enthalpy of the second preheater [kJ/kg] 101 Hmis is the bulk inlet enthalpy of the test section [kJ/kg] Qion is the heat loss in the unheated section [kW] Once the outlet enthalpy was determined, the inlet had to be calculated with another energy balance. To accomplish this, the heat flux for the preheater was required. The only measurements that were recorded for the power supplied to the second preheater during experiments was the RMS voltage (displayed on a digital voltmeter on the SCR Panel) applied to the tube itself. Since the test section also had RMS voltage measurements, the heat fluxes of the test section were calibrated with the RMS voltage reading, so that the heat flux of the preheater could be calculated. The square of the RMS voltage (FRMS)2 is linear with total power £>totai • The total power should be independent of mass flow. To verify this, three equations were fitted: 0.0989 + 6.87187 x JO'5 (v^sf 0.65 kg/min £?totai = {0.10274 + 8.39084 x JO'5 (V^)2 J.20 kg/min (5.17) 0.07947 + 7.97194x J0~5 {v^)2 2.20 kg/min Due to complications in the experiments there was a noticeable difference in the three equations. Therefore each equation was used for each mass flow to calculate heat fluxes (total) for preheater two for the experimental runs. Using equation 5.16, substituting h^m for hmjS , and <2u>ui for Q^, the inlet enthalpy was calculated (corresponded to an inlet bulk temperature). The heat flux per metre was estimated by taking the total power and dividing it by the heated length of the preheater (4.06 m). With this heat flux SCHeat.f was used to model fouling in the second preheater. The salt deposition model with the highest rate (relative to the other models) of molecular diffusion to the walls (Model 2: No Nucleation) was used for all predictions. Table 5.8 contains the results. 102 Table 5.8: Model predictions investigating the possibility of salt deposition to the hot tube wall in the second preheater. Run Mass Flow Heat Tbuik Twall Outlet Cone. Inlet Cone. No. [kg/min] [kW/m] out[°Cl out[°Cl [wt%] [wt%] 1 1.21 1.07 375.8 379.1 0.644 0.652 2 0.66 0.67 379.5 382.3 0.488 0.652 3 1.20 0.59 373.7 375.9 0.595 0.595 4 2.22 2.40 372.6 378.1 0.595 0.595 5 0.68 0.24 372.3 374.0 0.595 0.595 9 0.62 0.46 372.9 376.4 0.408 0.408 10 1.23 0.75 364.7 368.3 0.408 0.408 11 2.16 1.25 365.5 369.0 1.066 1.066 12 0.70 0.52 366.2 370.2 1.066 1.066 13 2.18 1.25 364.1 367.7 0.195 0.195 14 0.63 0.52 367.5 371.9 0.195 0.195 The model predicted salt deposition in the preheater in only runs 1 and 2. For these experiments, the initial concentration of salt solution entering the test section was adjusted to the outlet concentration of the preheater, and the four models were used again to generate salt deposition profiles for the test section. The corrected graphs are contained in Appendix B (figures B12 and B13). The only significant change was in run 2, where the model predicted salt layer thickness was reduced by 30 %, and the peak location was shifted 0.5 m further along the test section. If any preheater fouling had occurred, it was expected in run 2, since it had the highest inlet bulk temperature of the test section (375.4 °C) and an uninsulated bend. The results from the correction for run 2, indicated that if fouling in the preheater occurred for all of the runs with the higher inlet bulk temperatures, the comparison between model predictions and experimental data would improve. It was difficult to assess the error in the calculations of heat loss and heat flux due to the lack of instrumentation on the preheater. However, with inlet and outlet bulk temperature thermocouples in the preheater, the validity of the calculations could be checked. 103 5.5.2 Supersaturation in the Test Section In the majority of the results (figures B3 - B13), all deposition models (except Chan et al.) predicted exactly the same profile. Only in runs 9 and 14 was there an increase in molecular diffusion deposition from Model 2 with no bulk nucleation. The 'Complete' model (with particle deposition) predicted no increase in fouling rate compared to the same model without particle deposition (Model 1: 'Suspended Particles'). To investigate the possibility of supersaturation of the bulk fluid (which is important in nucleation theory) the ratio of dissolved salt concentration to bulk solubility was calculated and plotted for all experiments. Figure 5.11 showed that in all runs, except 9 and 14, the bulk fluid never exceeded the solubility limit (ratio < 1). This implied that particle formation and deposition was not an important factor for the model predictions of our experimental conditions. It is interesting to note that Runs 9 and 14 had the two highest outlet bulk temperatures (387.6 and 388.5 °C) and therefore wall temperatures. Particle formation and deposition was not important, and may only be a factor when the concentrations of the salt solutions are very low (< 10'3 wt%). Figures 5.12 and 5.13 are model-predicted deposition profiles for run 14 that have been extended for one and two test section lengths, to examine the fouling rates at the lower concentrations. It is only after the dissolved concentrations have dropped to 10"5 wt% and bulk particle concentrations have accumulated to 2 x 10"2 wt% (figure 5.13) that particle deposition is the dominating mechanism (bulk temperature from 420 - 500 °C in these cases). With the concentrations so low at this point, the salt thicknesses generated are extremely thin and are negligible when compared to the earlier thicker section of the profile. 5.5.3 Salt Layer Location, Peak Thickness, and Shape Table 5.9 contains results comparing heights y and axial location z of the peak. Additionally the data from table 5.9 has been graphed in figure 5.14, which was grouped by the inlet bulk temperature of the experimental run. Figure 5.15 was generated to 104 • Run 1 —B--Run2 Run 3 —A- Run 4 — A - Run 5 — • - -Run 9 —e--Run 10 —X -Runll —x--Run 12 -Run 13 —©-Runl4 1 2 Axial Distance [m] Figure 5.11: Saturation of the solution along the test section for salt deposition experiments with Na2S04 at 25 MPa and sub- to supercritical temperatures. 105 3.0 3.5 4.0 4.5 5.0 Axial Distance [m] 5.5 6.0 -o— Suspended Particles No Nucleation —A— Complete Figure 5.12: Model predictions for run 14, extended by another test section length to compare the molecular and particle deposition rates. in CD O •4-> 6.0 6.5 7.0 7.5 8.0 Axial Distance [m] 8.5 9.0 Suspended Particles -e— No Nucleation Complete Figure 5.13: Model predictions for run 14, extended by two test section lengths to compare the molecular and particle deposition rates. 106 Table 5.9: Comparison between model predictions and experimental data of the peak heights and location of the salt layer. Run Models 1, 2 and 4 Chan et al. Zmodel " Zexp y model y model [m] Yexp [m] Yexp 1 -0.75 2.80 -0.55 5.50 2 -0.22 5.47 -0.28 7.00 3 -0.90 1.79 -0.80 3.67 4 -0.71 1.80 -0.91 3.33 5 -0.60 1.92 -0.70 4.25 9 -1.00 0.54 -0.70 1.27 10 -0.78 0.81 -0.58 1.77 11 -0.81 0.72 -0.61 1.77 12 -0.32 0.76 -0.22 2.00 13 -0.95 0.83 -0.15 1.47 14 -1.08 0.70 -0.48 1.43 examine the results when inlet bulk temperatures for the test section were 365 °C (possibility of fouling in the preheater was very small, even with a large error in the estimate of the heat loss in the tube bend, see section 5.5.1). In all runs the simplest model ('Chan et al.') over-predicted the peak thickness at an earlier axial location in the test section (except run 2). The peak height thickness ranged from 1.5 to 7 times the experimentally determined value. The other models also predicted the peak of the salt layer earlier than the experimental results, but the height discrepancy was less, ranging from V2 (many of the runs were actually under-predicted) to 4 times the height. The model prediction for run 2 was the only case where the peak location was later than the experimental location. This was because the actual salt layer deposited was very thin and had no definite peak (see figure B13), so the largest salt thickness was chosen and designated as the peak height. Also, run 2 had less thermocouples than the other runs, so a peak height may have been missed. From these results, it appeared that Models 1, 2 and 4 predicted peak heights that were much closer to the experimental data. As mentioned previously, the prediction of peak heights would be 107 1 7.00 6.00 5.00 --o, 4.00 ^3.00 2.00 --1.00 -0.00 • -1.1 -0.9 -0.7 -0.5 -0.3 -0.1 Zmodel - Zexp [m] • Models 1,2 and 4 (High Bulk) • Chan et al (High Bulk) o Models 1,2 and 4 (Low Bulk) o Chan et al (Low Bulk) 0.1 0.3 Figure 5.14: Comparison of the height and location of the peak of the salt layer. Hi 0 1 o. 2.00 1.80 1.60 1.40 1.20 1.00 0.80 0.60 0.40 0.20 0.00 o o o o + -1.1 -0.9 -0.7 -0.5 -0.3 -0.1 0.1 Zncdel " Zexp [m] o Models 1,2 and 4 (Low Bulk) o Chan et al (Low Bulk) 0.3 Figure 5.15: Comparison of the height and location of the peak of the salt layer. 108 very important in determining how long a tubular reactor could run before the deposits completely blocked the fluid flow. 'Chan et al.' was not very accurate in predicting peak heights, and though in previous experiments at Sandia the model was in agreement with experimental results (section 2.5.2.3), it was at a much lower flow rate (0.036 kg/min) than the conditions used in this study (0.65 - 2.20 kg/min). If 'Chan et al.' was used for predicting fouling rates, the results would be overestimated. All experimental runs with lower inlet bulk temperatures (figure 5.15) had better correlation between peak heights. This again emphasizes the fact that the lower inlet bulk temperatures for these runs produced improved results. Though preheater fouling was not determined for all runs 1-5 (with heat loss estimation that was used, see section 5.5.1), it seems to be the most likely case for the large discrepancy. However, the difference in axial location of the peak, between model and experimental results, was approximately the same for runs 1-5 and 9-14. Figures B3 - B13 are referred to for analysis of the shape of the deposition profiles. For 'Chan et al.' the start of the deposits were very abrupt (peak heights within two length-steps zlz of the beginning of the layer), due to the first deposits occurring when the decreases in the solubility limit dCM/dz were largest in concentration. 'Chan et al.' was also the most sensitive to the non-continuous slope of the solubility curve fit. This was demonstrated in runs 9, 10 and 13, with small 'bumps' in the layer after the peak height. The 'bumps' occurred when the model calculated the salt deposits with two solubility points that straddled the transition point between the last two sections of the curve fit. This amplified the non-continuous nature of the slopes, depositing more salt than in the preceding step. 109 Models 1, 2 and 4 all had almost exactly the same shape. Only in runs 9 and 14 did 'No Nucleation' exhibit an increase in deposition near the end of the test section. The more gradual increase and decrease of the salt layer profiles was similar to the experimental data. Therefore, the molecular diffusion rate generated a salt layer that was similar in shape, but at an earlier axial location than the experimental. The discrepancy in location could be due to errors in the solubility equation (see section 5.5.4). For runs 1 - 5 the heat fluxes for each mass flow were all lower than runs 9-14, and this generated thinner, longer salt layers. Therefore keeping heat fluxes as low as possible in the region where the solubility limit is first exceeded could extend the running time of a facility before shutting down for cleaning. A SGWO reactor that has internal heating due to the exothermic reaction, may require cooling to keep the temperature increase gradual. Additionally a more gradual slope of the salt layer reduces pressure losses that can occur from abrupt flow restrictions. 5.5.4 The Effect of a ± 1 °C Error in the Solubility Curve on the Model Predictions for Salt Deposition An important error that was considered was the effect that the temperature error associated with the solubility curve had on the model predictions. The bulk temperature measurements made during the solubility experiments (which attempted to keep the test section isothermal) were examined, and the inlet to outlet temperature varied between 0.5 and 1.5 °C. An error of + 1 °C was assigned to the solubility curve, and the model predictions for run 10 were repeated using only two salt deposition models; Model 1: Suspended Particles, and Model 3: Chan et al. The results are displayed in figure 5.16. The error was implemented into the model predictions by adding or subtracting 1 °C from the temperature that was being used to determine the solubility limit in the computer program. Therefore the '+ 1' model predictions assume that the temperatures were under-estimated by 1 °C in the solubility experiments. This is shown in figure 5.16, as both (Suspended Particles and Chan et al.) '+1' salt layer predictions start earlier in the 110 Run 10: Solubility Limit Error Figure 5.16: Effect ofa+1 °C temperature error in the solubility curve on the model predictions. test section (compared to figure B7). Conversely, the model predictions assume that the temperatures were over-estimated by 1 °C in the solubility experiments, and consequently all salt layers start later in the test section. The difference in axial location between the modified runs for each model was approximately 0.5 m. With such a large location shift, if the temperature error was larger (3 °C), the difference in peak location between the predicted and experimental profiles could be resolved. Such a large error was possible, since many of the solubility experiments were run without insulation on the tube bend between the preheater and the test section. Similar to the problem in the deposition experiments, higher temperatures than the isothermal test section (for solubility experiments) may have been present in the preheater. Ill There was a large change in peak height for the 'Chan et al.' predictions (in the '+1' case the tube 'plugged'). This was due to the model's peak height sensitivity to the solubility limit. The experimental conditions for run 10 were in the critical region (rapid decrease in solubility), so shifting the solubility curve with a temperature error had a substantial affect on the peak height. This was not as noticeable with Model 1. From these results it was obvious that the accuracy of the solubility curve was the most important factor in predicting salt deposition profiles. Solubility data in this study were considered accurate when compared to previous data which were fairly scattered. There was also less than a ± 8% error in concentration for the assumption of 'adequate residence time' in the test section (section 5.3.5). Maintaining an accurate, isothermal test section is key to determining the solubility curve for sodium sulphate in water. 5.5.5 Comparison Between the Model-Predicted and Experimentally Measured Pressure Drop Along the Fouled Test Section The pressure drop measurements from the differential pressure cells (DP 427 and DP 429) were plotted (figure 5.17) with the model predictions against the mass flow of water used in each experimental run. The majority of the model predictions were several orders of magnitude higher than the experimental data. Predictions by 'Chan et al.' were especially high with the largest peak heights of all the models. Also as expected, the increase in mass flow increased all pressure drop measurements and predictions (equation 5.9). The method for calculating pressure drop in a fouled tube used the salt layer thickness as the tube roughness. Additionally, the program used the reduced diameter to calculate the velocity of the fluid and pressure drop. This was found to be inconsistent, since the assumed tube roughness value was in some cases larger than the radius through which fluid was flowing. So as the thickness of the salt layer approached the radius of the 112 100000 17 10000 2a o Q l-i t/3 1/3 OH 1000 100 10 1 • • A A s A A s • A B \ A \ < o 6 O 1 — i 1 1 0.0 0.5 1.0 1.5 Mass Flow [kg/min] 2.0 2.5 A Models 1, 2 and 4 a Chan et al. • Experimental ° Clean Tube Figure 5.17: Comparison between the model predicted and the experimentally measured pressure drop along the fouled test section. tube ('Chan et al.'), the model-predicted pressure drop increased extremely rapidly. Therefore, the model predictions should have been more accurate with very thin salt layers. This was proved correct since the most accurate comparison was run 2 (model data points around 10 kPa, 0.6 kg/min, experimental data point 6.6 kPa), which had the thinnest layer of salt (< 0.1 mm) in all the experimental runs. The experimental pressure drop measurements of the fouled tube were approximately an order of magnitude larger than the pressure drops of the clean tube. This indicates that the salt layer does have an effect on the frictional losses, but the roughness is not directly proportional to the thickness. It was noticed during the experiments that just after the start of the fouling period, the differential pressure was increasing slowly, approximately 10 kPa after several minutes. As the fouling period increased in time (salt layer grew thicker), the pressure 113 drop increased at an accelerated rate (10 kPa after several seconds). Since overall pressure drop is a function of many parameters of the system (tube diameter, tube roughness, mass flow, salt deposit structure, etc.), perhaps the rate that the pressure drop is increasing is more descriptive than the differential pressure measurement in determining how close a tube is to fouling completely closed. The error associated with the differential pressure measurements was large. To begin with the calibration was performed twice, each with different results. The calibration that was chosen for experiments had a full scale reading of 9 volts at 55 kPa, compared to a rated full scale reading of 10 volts at 55 kPa. Also during experimental runs, the measurements would fluctuate as much as 2 volts (-10 kPa) with a clean tube and steady state conditions (these fluctuations stopped when the temperature was near critical). But even these large errors do not account for the orders of magnitude difference between the model predictions and the experimental measurements. From these results it appears that pressure drop measurements in a SCWO system can give a qualitative indication of fouling, though it is not clear how the salt layer affects the ffictional losses. 114 6. Conclusions A salt deposition model was developed for fouling of a heated tube from a sodium sulphate - water solution. Experiments were completed in a SCWO pilot plant at UBC and compared to the model predictions. Through this study the following conclusions were made. From solubility experiments completed with the SCWO pilot plant, the solubility of sodium sulphate in water at 25 MPa and in the temperature range of 370 - 500 °C was determined. The results compared well to experimental data from other researchers at sub-critical temperatures. The solubility decreases rapidly at the pseudo-critical temperature (385.0 °C at 25 MPa) and then less rapidly once the critical temperature is exceeded. Also the solubility appears to reach a lower limit of approximately 5 x 10'5 wt% at 500 °C. The error in bulk temperature measurements (± 1 °C), incorporated into the solubility curve that was fitted to the data, had a large effect on the model-predicted salt deposition profiles. Computer modelling of deposition from a sodium sulphate-water solution in a heated tube was completed in conjunction with salt deposition experiments in an experimental test section in the SCWO pilot plant. The experiments involved forming salt layers in the test section as salt deposited from a sodium sulphate - water solution at various conditions (salt solution concentration, heat flux, flow rate). Salt deposition profiles were inferred from outside surface temperature measurements of the tube and compared to model predictions. During the analysis, the thermal conductivity of sodium sulphate was inferred from experimental temperatures and overall mass balances to be in the range of 2.5 to 9.8 kW/m-K, with an average of 5.8 kW/m-K. Four simple deposition models were compared with the measured profiles. From the comparison, it was clear that the profiles were influenced by mass transfer limitations and wall temperature in addition to the bulk solubility. 115 Models differing in their treatment of particulate salt were not differentiated for the experimental conditions of this study because the bulk saturation ratio rarely exceeded 1, according to the models. This last conclusion is dependent on the mass transfer coefficients near the critical point, which must be considered quite uncertain. Nevertheless, there was good agreement between the measured salt thicknesses and predictions based on convective diffusion of single salt molecules to the hot wall, without any surface reaction resistance. Finally the assumption that roughness is equal to salt layer thickness clearly exaggerated model-predicted pressure drops. Experimental results of fouled tubes when compared to clean tubes, indicated that there is an increase in ffictional losses due to the salt layer, but this cannot be estimated accurately through the chosen assumption. 116 7. Recommendations The UBC SCWO facility has the capability to run salt deposition experiments in near critical water. However, during the course of this study it became evident that many improvements could be made to increase the accuracy of measurements and decrease the difficulty in determining fouling rates. To begin with instrumentation should be added to the second preheater to monitor temperature, so that salt deposition can be avoided. This should improve the accuracy of the model predictions when compared to the experimental data. Once this is done, experimental runs 1-5 (with high inlet temperatures at the test section) should be reproduced to see if there was fouling occurring in the preheater for those specified conditions. A sampling line should be installed immediately after the test section, so that real-time effluent measurements (conductivity) can be made without the long residence time of the regenerative heat exchanger influencing steady state conditions. Additionally, larger (110 kPa) differential pressure diaphragms should be used for the longer fouling experiments, with thicker deposits. Besides improvements on the SCWO facility itself, there are some recommendations for future salt deposition studies. Detailed mass balance studies should incorporate the time scales of the system, so that delivery and collection times are more accurate. The results should indicate if any accumulation of salt is occurring in the system between experiments. Solubility experiments should be performed at lower flow rates (< 0.65 kg/min) with sodium sulphate, especially near critical temperatures to verify the accuracy of the curve fitted in this study. During the solubility experiments, the accuracy of the thermocouple measurements (both wall and bulk) must be checked, since a ± 1 °C error had a large affect on the salt deposition modelling. Salt deposition experiments with sodium sulphate should focus on the comparison between molecular diffusion and particle deposition. Particular attention should be placed on the selection of the mass transfer coefficient hm which (in this study) is from work which does not properly incorporate the large property variations from the bulk fluid to the wall found in the critical region. Experiments with sodium chloride, a salt that has been used in many more experiments, 117 should use similar methods of determining salt layer thicknesses, and effluent concentrations. To commercialize the SCWO process, there are still many problems with salt deposition that need to be addressed. From this study, several important ideas have been formulated. To begin with, fouling rates are most affected by how quickly the solubility limit is decreasing. Larger decreases in solubility (axially along the tube) will produce larger peak heights of the salt layer (reducing time of operation without fouling problems). Since the solubility limit is directly related to temperature, in a SCWO reactor it would be favourable to have small axial temperature gradients, especially near the critical region where the solubility limit is decreasing the fastest. Small temperature gradients distribute a salt layer over a greater tube length, creating longer, thinner deposits (increasing the time a facility can operate, until it must be shut down to clean out the salt deposits). For a tubular reactor, the heat flux should be kept low. By keeping the heat flux low, the bulk to wall temperature difference (solubility difference) is low, and since mass diffusion to the walls relies on concentration gradients, the rate of molecular deposition can be limited. For the case where the oxidation reaction is producing heat, the reactor may have to be cooled externally. 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McGraw-Hill, Inc., Second Edition, 1986 Yamagata, K., Nishikawa, K., Hasegawa, S., Fujii, T., and Yoshida, S., "Forced Convective Heat Transfer to Supercritical Water Flowing in Tubes", International Journal of Heat and Mass Transfer, v 15, 1971, 2575-2593 123 Appendix A Thermocouple Position on the Heated Area of Test Section The bulk thermocouples are B2 - B4, the surface thermocouples are SI - S20 Table Al: Heated distance from the first cable clamp of the bulk and surface temperature thermocouples on the test section Thermocouple Axial Position [m] B2 0 SI 0.063 S2 0.209 S3 0.350 S4 0.496 S6 0.715 S7 0.853 SS 1.024 S9 1.218 SIO 1.407 B3 1.473 Sll 1.551 S13 1.897 S16 2.278 S17 2.414 S18 2.551 S19 2.69 S20 2.822 B4 2.946 124 Appendix B Comparison of the Model-Predicted and Experimental Salt Deposition Profiles The following appendix contains graphs of the salt deposition profiles from both model predictions and experimental data. There are 13 figures (Bl - B13). The last two figures (B12 and B13) are corrected model predictions for runs 1 and 2 (figures Bl and B2). All model predictions were generated by a computer program called SCHeat.f, written in FORTRAN-77, and complied on a Pentium 75 MHz personal computer. 125 Run 1 1.2 -i 0.0 0.5 1.0 1.5 2.0 2.5 3.0 Axial Distance [m] —B—Suspended Particles—e—No Nucleation —A—Chan etal. —H—Complete • Bperimental Figure Bl: Comparison between model and experimental data for Run 1 Run 2 Axial Distance [m] —B—Suspended Particles —e— No Nucleation —A— Chan etal. —X—Complete • Dq)erimental Figure B2: Comparison between model and experimental data for Run 2 126 Run 3 1.2 Axial Distance [m] •e— Suspended Particles —e— No Nucleation —A— Chan etal. —x—Complete • E>perirnental Figure B3: Comparison between model and experimental data for Run 3 Run 4 1.2 T Axial Distance [m] •e—Suspended Particles —©—No Nucleation —A—Chan etal. X Complete • B-perimental Figure B4: Comparison between model and experimental data for Run 4 127 Run 5 1.8 Axial Distance [m] •B— Suspended Particles o No Nucleation A Chan et al. X Complete • Experimental Figure B5: Comparison between model and experimental data for Run 5 Run 9 3.0 Axial Distance [m] •e—Suspended Particles —e—No Nucleation —A—Chan et al.—x—Complete • Ejqjerimental Figure B6: Comparison between model and experimental data for Run 9 128 Run 10 0.0 0.5 1.0 1.5 2.0 2.5 3.0 Axial Distance [m] -^B—Suspended Particles —o—No Nucleation —A— Chan etal. —X—Complete • Ejperirnental Figure B7: Comparison between model and experimental data for Run 10 Run 11 2.5 -T Axial Distance [m] •e—Suspended Particles —e— No Nucleation —A—Chan etal. —x— Complete • Btperirnental Figure B8: Comparison between model and experimental data for Run 11 129 Run 12 Axial Distance [m] •e—Suspended Particles —e—No Nucleation —A—Chan etal. —X—Complete • Experimental Figure B9: Comparison between model and experimental data for Run 12 Run 13 0.0 .0.5 1.0 1.5 2.0 2.5 3.0 Axial Distance [m] —B—Suspended Particles —o—No Nucleation —A—Chan etal. —X— Complete • Experimental Figure B10: Comparison between model and experimental data for Run 13 130 Run 14 0.0 0.5 1.0 1.5 2.0 2.5 3.0 Axial Distance [m] •e— Suspended Particles o No Nucleation —A— Chan et al. x Complete • Byerimental Figure Bll: Comparison between model and experimental data for Run 14 131 Run 1: Corrected for Preheater Fouling 0.0 0.5 1.0 1.5 2.0 2.5 3.0 Axial Distance [m] —a—Suspended Particles —e—No Nucleation — A — Chan et al. — x — Complete • Experimental Figure B12: Run 1 model predictions correctedfor preheater fouling. Run 2: Corrected for Preheater Fouling 1.0 -| •—, 0.9 § 0.8 --Axial Distance [m] •B—Suspended Particles —e—No Nucleation — A — Chan et a l . —X— Complete • Experimental Figure B13: Run 2 model predictions correctedfor preheater fouling. 132 Appendix G Comparison of the Model-Predicted and Experimental Salt Deposition Profiles for a Modified Mass Transfer Coefficient As a sensitivity test for the model predictions, the power of the Lewis number in equation 3.17 was modified from 0.387 to 0.613 to see the effect on the calculation of the mass transfer coefficient. The model predictions of the experimental runs are contained in figures C1..C13. The mass transfer coefficient varied from -8% to +19 % of the unmodified calculations. 133 Run 1 1.2 -| Axial Distance [m] —e—Suspended Particles —e—No Nucleation —A—Chan et al. —K— Complete • Experimental Figure CI: Comparison between model and experimental data for Run J Run 2 1.0 Axial Distance [m] Suspended Particles—e—No Nucleation —A—Chan et al. —*—Complete • Experimental Figure C2: Comparison between model and experimental data for run 2. 134 Run 3 1.2 -i Axial Distance [m] •B— Suspended Particles —e— No Nucleation —A— Chan et al. —x— Complete • Bperimental Figure C3: Comparison between model and experimental data for run 3. Run 4 1.2 -r Figure C4: Comparison between model and experimental data for run 4 135 Run 5 1.8 Axial Distance [m] •e—Suspended Particles —e— No Nucleation A Chan et al. X Complete • Experimental Figure CS: Comparison between model and experimental data for run 5. Run 9 3.0 0.0 . 0.5 1.0 1.5 2.0 2.5 3.0 Axial Distance [m] Suspended Particles —e—No Nucleation —A—Chan etal. —X—Complete • Experimental Figure C6: Comparison between model and experimental data for run 9. 136 Run 10 2.5 Axial Distance [m] •B—Suspended Particles —o— No Nucleation —A— Chan etal. —X—Complete • Ejperirnental Figure C7: Comparison between model and experimental data for run 10. Run 11 2.5 -i Axial Distance [m] e— Suspended Particles —e— No Nucleation —A— Chan et al. —X— Complete • Bperimental Figure C8: Comparison between model and experimental data for run 11. 137 Run 12 Axial Distance [m] •a— Suspended Particles —©—No Nucleation —A— Chan etal. —X— Complete • Experimental Figure C9: Comparison between model and experimental data for run 12. Run 13 Axial Distance [m] Suspended Particles —©—No Nucleation —A—Chan etal. —X— Complete • Experimental Figure CIO: Comparison between model and experimental data for run 13. 138 Run 14 0.0 0.5 1.0 1.5 2.0 2.5 3.0 Axial Distance [m] -B— Suspended Particles o No Nucleation —A— Chan et al. x Complete • Experimental Figure Cll: Comparison between model and experimental data for run 14. 139 Run 1: Corrected for Preheater Fouling 1.2 T 0.0 0.5 1.0 1.5 2.0 2.5 3.0 Axial Distance [m] e—Suspended Particles —©—No Nucleation a Chan et al. —X— Complete • Experimental Figure C12: Run 1 model predictions correctedfor preheater fouling. Run 2: Corrected for Preheater Fouling 1.0 -i 0.9 --§ 0.8 --0.0 0.5 1.0 1.5 2.0 2.5 3.0 Axial Distance [m] •e—Suspended Particles—e—No Nucleation —A— Chan et al. —X— Complete • Experimental Figure C13: Run 2 model predictions correctedfor preheater fouling. 140 Appendix D Data Files for the Experimental Runs and Results For all of the data files, any part of the file name {date} that has the following format refers to a date: a22#l = August 22, experimental run #1 on that date ap = April, m = May, j = June, jy = July Table Dl: Summary of the data files Area File Description Heat Transfer HL{date}.xls Heat loss experiments Solubility CurveFit.xls Solubility curve fit with data curvhigh.obj Curve fit for the high region of the solubility curve curvmid.obj Curve fit for the middle region of the solubility curve curvlow.obj Curve fit for the low region of the solubility curve SOL{date}.xls Solubility experimental data files SOLNa2SC4.xls Solubility graphs for sodium sulphate SOLNaCl.xls Phase diagram for sodium chloride Salt Deposition {date}.xls Salt deposition experimental data files Effluent.xls Concentration of effluent during salt deposition experiments EqualMass.xls Calculations to determine time to deliver 24 g of salt for each experimental run Extended.xls Graph of salt deposition profiles for extended test section k{date}.xls Thermal conductivity data mass{date}.xls Mass balance data outlineZ99.xls Outline of normalizing the data for comparison between experimental salt deposition profiles Peak.xls Graph of peak of salt layer data Phoutline.xls Outline of the preheater fouling problem Profilesl.xls Salt deposition profile graphs (Figures B1..B11) Profiles2.xls Salt deposition profile graphs for increased mass transfer coefficient (Figures C1..C11) saltZ99#l.xls Comparison between experimental salt deposition profiles saltZ99#2.xls Comparison between experimental salt deposition profiles SDerrors.xls Graphs for runs 1 and 2 corrected for preheater fouling and solubility curve error effect on model predictions SDOutline.xls Outline of salt deposition experiments Supersat.xls Graph of supersaturation ratio tempZ99#l.xls Comparison between experimental temperature profiles tempZ99#2.xls Comparison between experimental temperature profiles Pressure Drop DPGraph.xls Graph of differential pressure drop results 141 Appendix E Buoyancy Calculations Buoyancy effects in the tube were checked with the following criterion (Adebiyi and Hall, 1975): A = Grb Reh-2-75Prb-°-5[l+2.4Reb1/8(Prh2/3 - /)] 7 ( E. 1) with Reynolds and Prandtl calculated with equations 2.5 and 2.6, and the Grashof number calculated with: To neglect buoyancy effects, A < 3 x 10"5. For typical conditions of this study: r b = 40oc r w = 42oc /w=0.33kg/s pb = 166.63 kg/m3 dp/dT= 3.017 kg/m3-K d= 0.006272 m p = 29 x 10"* kg/s-m ^=9.81 m/s2 Prb = 2.273 Reb = 233337 Grb = 28924945 Substituting these values into equation E. 1 calculates a value for A = 2.4 x 10'8. Since this is less than 3 x 10"5, buoyancy can be neglected. 142 Appendix F Source Code for the Computer Programs SCHeatf and Saltf The foHowing appendix contains the source code for SCHeat.f, a computer program that models the heat transfer and salt deposition of a sodium sulphate and water solution flowing through a heated tube. Additionally the source code for Saltf, a computer program that converts outside surface temperatures to salt layer thicknesses is also contained in this appendix. All programs were written in FORTRAN-77. 143 Computer Program SCHeat. Q ******************************************************************** PROGRAM SCHEAT Q ******************************************************************** C Simulating Heat Transfer and S a l t Deposition i n a Heated Tube Q ******************************************************************** C Q ************************* C Declaration of Var i a b l e s Q ************************* C C AREA = cross s e c t i o n area of the tube [m"2] C BOLTZ = Boltzman's constant [J/K] C C = the i n i t i a l concentration of s a l t i n the f l u i d [wt%] C CB = concentration of d i s s o l v e d s a l t i n the bulk [wt%] C - i n d i c e i s the step number C CBP = the concentration of s a l t p a r t i c l e s i n the bulk [wt%] C - i n d i c e i s the step number C CBPW = the concentration of s a l t p a r t i c l e s at the wall [wt%] C CP = s p e c i f i c heat capacity [kJ/kg-K] C CPW = s p e c i f i c heat capacity using wall p r o p e r t i e s [kJ/kg-K] C CSAT1 = Na2S04 s o l u b i l i t y bulk temp.previous step [wt%] C CSAT2 = present step [wt%] C CSATW = Na2S04 s o l u b i l i t y at TW2 wall temp. [wt%] C D = den s i t y of flow [kg/m"3] C DBB = den s i t y of bulk f l u i d [kg/m"3] C DDDT = den s i t y gradient w.r.t. temperature [kg/nT3-K] C DH = the d i f f e r e n c e i n enthapies between two steps [kJ/kg] C DIA = diameter of the tube [m] C DIA2(ICOUNT) = an array to index the diameters at each [m] C a x i a l step along the tube length C DIAFOUL = diameter of tube with f o u l i n g [m] C DIAMOL = diameter of molecule of Na2S04 [microns] C DIAPART = nucleated p a r t i c l e diameter [m] C DIFF = molecular d i f f u s i v i t y [m"2/s] C DTE = d i f f e r e n c e between TE and TE2 [K] C DTIME = time st e p s i z e [hours] C DTW = the absolute d i f f e r e n c e between two wall [K] C temperatures c a l c u l a t e d d i f f e r e n t l y C DTWALL = d i f f e r e n c e between i n s i d e wall temperatures of [K] C two d i f f e r e n t c o r r e l a t i o n s C DTWTB = the d i f f e r e n c e between TWTB2 and TWTB used f o r [K] C i t e r a t i o n f o r convergence of TWTB C DV = v e l o c i t y d i f f e r e n c e [m/s] C DW = den s i t y of f l u i d at i n s i d e wall temperature [kq/m"3] C DZ = s t e p s i z e along the tube length [m] C EPS = ep s i l o n , roughness of tube [mm] C EPSFOUL = roughness corrected with p a r t i c l e d e p o s i t i o n [mm] C F = f r i c t i o n f a c t o r [-] C FCLEAN = f r i c t i o n f a c t o r of a clean tube [-] C FFOUL = f r i c t i o n f a c t o r a f t e r f o u l i n g [-] C FLOW = massflow of water [kg/s] C FLOW2 = massflow of water [kg/min] C FLOWMOL = molecular t r a n s f e r rate [kg/s] C FLOWPART = p a r t i c l e t r a n s f e r . r a t e [kg/s] C FLOWSALT = s a l t d e p o s i t i o n rate [kg/s] C FOULPRESS = pressure drop a f t e r f o u l i n g : [Pa/10] C - i n d i c e i s the step number C HI = enthalpy of previous step [kJ/kg] C H2 = enthalpy of present step [kJ/kg] C HM = mass t r a n s f e r c o e f f i c i e n t [m/s] C HW = enthalpy at the wall temperature [kJ/kg] C ICOUNT = counter f o r indexing tube diameters [-] C ICOUNT2 = counter used to set the i n i t i a l s a l t [-] C nucleation wt% C ICOUNT4 = counter used to set the i n i t i a l s a l t [-] C nucleation wt% C K = thermal c o n d u c t i v i t y [mW/K-m] 144 C K625 = thermal c o n d u c t i v i t y of Inconel 625 at TK [W/K-m] C K6252 = thermal c o n d u c t i v i t y of Inconel 625 at TTK [W/K-m] C KH20 = thermal c o n d u c t i v i t y of water used [W/K-m] C i n c a l c u l a t i o n of l a y e r C KSALT = thermal c o n d u c t i v i t y of Na2S04 c a l c u l a t e d [W/K-m] C from mass balance runs C KLAYER = thermal c o n d u c t i v i t y of s a l t l a y e r [W/K-m] C i n c l u d i n g p o r o s i t y f a c t o r C KW = thermal c o n d u c t i v i t y using wall temp, pr o p e r t i e s [mW/K-m] C KW2 = using TW2 c a l c u l a t e d from f i l m average [mW/K-m] C pr o p e r t i e s TWTB2 C MODEL = index for s a l t d e p o s i t i o n model used [-] C P = pressure of the water [MPa] C PDROP = a c c e l e r a t i o n a l pressure drop [Pa] C PDROPTOT = cumulative a c c e l e r a t i o n a l pressure drop [Pa] C PHI = p o r o s i t y of the s a l t l a y e r [-] C PR = Prandtl number [-] C PRCLEAN = Prandtl number of clean tube [-] C PRW = using wall temp, pr o p e r t i e s [-] C PRESS1 = pressure drop up to previous step [Pa/10] C PRESS2 = pressure drop up to present step [Pa/10] C Ql = heat input per un i t length of tube [kW/m] C Q2 = heat input per un i t area of tube [kW/m"2] C RE = the Reynolds number of the flow [-] C RECLEAN = Reynolds number of clean tube [-] C REFOUL = Reynolds number with f o u l i n g [-] C REW = using wall temp, pr o p e r i t e s [-] C RI = i n s i d e radius of the tube [m] C RS = i n s i d e radius of tube with s a l t l a y e r [m] C RO = outside radius of the tube [m] C RUN = index f o r exp. run, to r e t r i e v e input data [-] C SUPERSAT = r a t i o of d i s s o l v e d s a l t to s o l u b i l i t y l i m i t [-] C T = temperature [K] C T l = temperature of previous step used i n gradient [K] C 12 - temperature of present step used i n gradient [K] C TB = temperature of bulk f l u i d [K] C TCHECK = used to f i n d T2 with H2 [K] C TCOUNT = used as a counter f o r the time loop [-) C TE = external wall temperature [K] C TE2 = r e c a l c u l a t i o n of external w a l l temperature [K] C TIME1 = running time of experiment f o r f o u l i n g [hours] C TIME2 = running time of experiment f o r f o u l i n g [s] C TK = temperature at which thermal c o n d u c t i v i t y f o r [K] C inconel 625 i s c a l c u l a t e d C TLE = Lewis number [-] C TLE = Lewis number with wall p r o p e r t i e s [-] C TLENGTH = length of the tube [m] C TNU = Nusselt number [-] C TNUW = using wall temp, p r o p e r t i e s [-] C TS = surface temperature under the l a y e r of s a l t [K] C TTK = average wall temperature [K] C TW = i n s i d e wall temperature [K] C TW2 = c a l c u l a t e d using TWTB2 (using wall temp, property [K] C v a r i a t i o n s C TWTB = TW - TB, d i f f e r e n c e between w a l l and bulk temp. [K] C TWTB2 = using wall temp, property v a r i a t i o n s [K] C TWSC = the i n s i d e wall temp, f o r the Swenson/Carver [K] C V = v e l o c i t y of the bulk f l u i d [m/s] C - i n d i c e i s the step number C VCLEAN = v e l o c i t y of f l u i d i n a clean tube [m/s] C VD = dep o s i t i o n v e l o c i t y [m/s] C VDENS = used to c a l c u l a t e the v e l o c i t y change [m/s] C due to de n s i t y changes C VISC = v i s c o s i t y [mg/s-m] C VISCW = using wall temp, p r o p e r t i e s [mg/s-m] C VPRESS = the dynamic pressure change from a v e l o c i t y [Pa] C change due to s a l t d e p o s i t i o n C YSALT = thickness of s a l t l a y e r on tube walls [mm] C YPART = thickness of s a l t l a y e r due to p a r t i c l e [mm] C layer C YMOL = thickness of s a l t l a y e r due to molecular [mm] C d i f f u s i o n C YTOT(ICOUNT) = an array to index the s a l t thickness [mm] C along the tube C Z = distance along the tube length [m] C Q ********** 145 c c c c c c c c c c c c c c c c c c c c c c c c c c Functions CDECREASE(CSAT,FLOWMOL,FLOW) DIFFUSE(T,VISC) ENTHALPY(HI,Ql,DZ,FLOW) FRICTION(RE,E PS,DIA) PRAN(VISC,CP,K) PRESSURE(F,DZ,FLOW,DIA,D,PRESS,VI,V2) RATEMASS(HM,DZ,DIA,DBB,CSAT2,CW) RATESALT(FLOW,CSAT1,CSAT2) REYN(FLOW,DIA,VISC) SALTTHICK(FLOWSALT,DZ,DIA,DTIME,PHI) SOLUBILITY(T) TCONDUCT(T,P) TINCONELK(TK) TLEWIS (K, D,CP, DIFF) TNUS1(RE,PR,DBB,DW) TRANSMASS(TNU,K,DIA,D,TLE,CP) TSALT(TS,Ql,KSALT,RS) TWTBFUN (Q2, DIA, TNU, K) TWOUT(TW,Q2,K625,RI,RO) VELOCITY(FLOW, D, DIA) VISCOSITY(T, P) IMPLICIT REAL*8 (A-H,K-M,O-Z) IMPLICIT INTEGER (I,J,N) DIMENSION DIA2(1000) DIMENSION YTOT(IOOO) DIMENSION EPSFOUL(IOOO) Na2S04 mass t r a n s f e r f o r Chan et c a l c u l a t e s d i f f u s i o n coef. c a l c u l a t e s enthalpy a f t e r dz c a l c u l a t e s f r i c t i o n f a c t o r Prandtl number pressure drop c a l c u l a t i o n molecular t r a n s f e r rate Chan et a l . s a l t d e p o s i t i o n rate Reynold's number c a l c u l a t e s the thickness of s a l t deposited Our s o l u b i l i t y curve thermal c o n d u c t i v i t y of water thermal c o n d u c t i v i t y of Inconel Lewis number uses Swenson/Carver c o r r e l a t i o n c a l c u l a t e s mass t r a n s f e r c o e f f . temperature through s a l t l a y e r c a l c u l a t e s Tw - Tb outside wall temperature v e l o c i t y of water v i s c o s i t y of water The following 'COMMON' EQTEST.F main program statements were included from the COMMON/CCPEQ/TCEQ,PCEQ,DCEQ COMMON/CSUB2/R,XMOL,TC,PC,DC COMMON/CNORM/TNORM,DNORM COMMON/CSUB3/TTR,PTR,DLTR,DVTR,TBOYL,PBOYL,DLB,DVB COMMON/COUT/NIN,NOUT INPUT / OUTPUT ON PC: NIN = 5 NOUT = 6 ****•*** + ****•*•* + ******* + **•* Reading i n the parameters WRIT£(NOUT,900) 900 FORMAT!/,' The following r e s t r i c t i o n s are applied to t h i s program: +',/,/,' A. The bulk temperature must be chosen so that there i s +no s a l t d e p o s i t i o n i n the f i r s t step and above 358 K.',/,' B. The +pressure must be 23-26 MPa.',/,' C. The f o u l i n g period must be +less than the plugging time of the tube.',/,' D. The i n i t a l bulk +temperature must be above 612 K, f o r the s o l u b i l i t y curve to be +valid') WRITE(NOUT,1001) 1001 FORMAT!/,' ENTER THE HEAT FLUX (kW/m]:M READ (NIN,*) Ql WRITE(NOUT,1002) 1002 FORMAT)/,' ENTER THE MASS FLOW [kg/min]:*) READ (NIN,*) FLOW2 WRITE(NOUT,1003) 1003 FORMAT!/,' ENTER THE BULK TEMP [K]:') READ (NIN,*) TB WRITE (NOUT,1005) 1003 FORMAT!/,• ENTER THE PRESSURE fMPa]:') READ (NIN,*) P WRITE (NOUT,1006) 1006 FORMAT!/,' ENTER THE LENGTH AND STEPSIZE [m] (separated by a comma + ) ' ) READ (NIN,*) TLENGTH,DZ WRITE(NOUT,1007.) 100"? FORMAT!/,' ENTER THE SALT DEPOSITION MODEL: ',//, 146 +' 1. SUSPENDED PARTICLES',/, +' 2. NO NUCLEATION',/, +' 3. CHAN ET AL.',/, +' 4 . COMPLETE') READ (NIN,*) MODEL WRITE(NOUT,1008) 1008 FORMAT!/,1 ENTER THE CONCENTRATION [wt%]:') READ(NIN,*) C WRITE(NOUT,1009) 1009 FORMAT)/,' ENTER THE FOULING TIME [s]:'.) READ(NIN,*) TIME2 C Q *********** C INPUT DATA Q *********** C C The thermal c o n d u c t i v i t y of sodium sulphate was determined C experimentally KSALT =5.8 TIME = TIME2/3600 DIA = 0.006272 PHI = 0.71 Q2 = Ql/(3.14159265359*DIA) FLOW = FLOW2/60 EPS = 0.002 C Q ****************************** C Opening F i l e f o r Data Storage Q ****************************** C OPEN (UNIT=7, FILE='SCHeatl.txt') C Q ********** C Time Loop Q ********** C • PI = 3.14159265359 YTOT(l) = 0 TCOUNT2 = 1 TCOUNT3 = 1 DTIME = TIME/10 TCOUNT = DTIME DO WHILE (TCOUNT3 .LE. 10) C Q ********************************** C C a l c u l a t i o n of i n i t i a l conditions Q ********************************** C T = TB C Functions BDENS and DENS are from EQTEST.f, the C thermodynamics program attached to SCHeat.f. . C BDENS i s used to get an i n i t a l estimate f o r C the de n s i t y and DENS get a more accurate value C with the estimate and a s p e c i f i e d accuracy C 'l.D-6' s i x decimal places DS = BDENS (T,P,0) D = DENS(P,T,DS,l.D-6) T l = T Dl = D C HB i s an enthalpy fu n c t i o n from EQTEST.f HI = HB (T, D) VISC = VISCOSITY(T,P) K = TCONDUCT(T,P) C CPB i s a s p e c i f i c heat fu n c t i o n from EQTEST.f CP = CPB(T,D) RE = REYN(FLOW,DIA,VISC) PR = PRAN(VISC,CP,K) PRESS1 = 0 PRESS2 = 0 FOULPRESS1 = 0 FOULPRESS2 = 0 DV = 0 VPRESS = 0 VPRESS2 = 0 PDROPTOT = 0 PDROP = 0 YSALT = 0 147 FLOWMOL = 0 FLOWPART = 0 CBP2 = 0 CBP1 = 0 VD = -0 TAUP = 0 TAUPPLUS = 0 USTAR = 0 TAUW = 0 VDSTAR = 0 SC = 0 VISCKIN = 0 CB2 = C CB1 = C SUPERSAT = 0 C Q **************************** C Simulation of Heat Transfer ICOUNT = 1 ICOUNT2 = 1 ICOUNT4 = 1 Z = DZ DO WHILE (Z .LE. TLENGTH) C Sets diameter to fouled diameter a f t e r the f i r s t C time, step with clean tube IF (TCOUNT .GT. DTIME) THEN DIA = DIA2(ICOUNT) EPS = EPS FOUL(ICOUNT) ELSE DIA = 0.006272 END IF ************************************************ C C C C a l c u l a t i n g the new Enthalpy (next length step) Q ************************************************ C CP = CPB(T,D) H2 = ENTHALPY(HI,Ql,DZ,FLOW) DH = H2 - HI DH2 = DH TCHECK = T C c C Loop to i t e r a t e to f i n d the temperature at the new enthalpy Q ************************************************************ C DO WHILE (DH2 .GT. 0.001) TCHECK = TCHECK + DH/CP DS = BDENS(TCHECK,P,0) D = DENS (P, TCHECK, DS, l.D-6) CP = CPB(TCHECK,D) HI = HB(TCHECK, D) DH = H2 - HI DH2 = ((DH)**2)**0.5 END DO T = TCHECK HI = H2 C Q ************************************* C R e c a l c u l a t i o n of p r o p e r t i e s at new T Q ************************************* C 9999 CONTINUE DBB = D DW = D D2 = D VISC = VISCOSITY(T,P) K = TCONDUCT(T,P) RE = REYN(FLOW,DIA,VISC) PR = PRAN(VISC,CP,K) C Q *************** C Swenson et a l . Q *************** C 148 C Swenson et a l . c o r r e l a t i o n i n i t i a l l y C estimated with bulk p r o p e r t i e s , due C to the f a c t that wall p r o p e r t i e s are C not known TNU = TNUS1(RE,PR,DBB,DW) TWTB = TWTBFUN(Ql,TNU,K) C Q **************** C Wall Properties Q **************** C 10 CONTINUE TW = T + TWTB DSW = BDENS(TW,P,0) DW = DENS(P,TW,DSW,l.D-6) HW = HB(TW,DW) CPW = CPB(TW,DW) C Wall p r o p e r t i e s f o r the Swenson C et a l . c o r r e l a t i o n which uses wall and C bulk p r o p e r t i e s f o r RE and PR KW = TCONDUCT(TW,P) VISCW = VISCOSITY(TW,P) REW = REYN(FLOW,DIA,VISCW) PRW = (HW - H21/TWTB * VISCW/KW TNUW = TNUS1(REW,PRW,DBB,DW) C Second c a l c u l a t i o n of wall temperature TWTB2 = TWTBFUN (Ql,TNUW,KW) TW2 = T + TWTB2 C Q *********************************************************** C I t e r a t i o n for convergence on the wall and bulk temperature C d i f f e r e n c e TWTB Q *********************************************************** C DTWTB1 = ((TWTB2 - TWTB)**2)**0.5 IF (DTWTB1 .GT. 0.01) THEN TWTB = TWTB2 GOTO 10 END IF 11 CONTINUE C Converts a l l temperatures to degrees C e l s i u s C Note: the TW here was determined from TWTB, so the C c a l c u l a t i o n of TWTB2 that stops the i t e r a t i o n s i s C not used i n c a l c u l a t i n g TW CT = T - 273.15 CTW = TW - 273.15 C CTS i s the temperature of the surface of the s a l t l a y e r C i n contact with the bulk f l u i d . When there i s no C f o u l i n g TS = TW. I f there i s f o u l i n g , a l l c a l c u l a t i o n s C up to t h i s point are have been done with the fouled diameter. C Therefore, TW = TS and the actu a l i n s i d e w a l l temperature C i s c a l c u l a t e d l a t e r i n the outside surface temperature s e c t i o n . CTS = TW - 273.15 C Q **************** C S a l t Deposition Q **************** C Q ******************* C I n i t i a l Conditions (2 ******************* C DS = BDENS(TW,P,0) DW = DENS(P,TW,DS,l.D-6) CP = CPB(T,DBB) KW = TCONDUCTITW,P) VISCW = VISCOSITY(TW,P) DIFFW = DIFFUSE(TW,VISCW) REW = REYN(FLOW,DIA,VISCW) PRW = (HW - H2)/TWTB * VISCW/KW TNUW = TNUS1(REW,PRW,DBB,DW) CPW = (HW-H2)/TWTB TLEW = TLEWIS(KW,DW, CPW, DIFFW) CSAT2 = SOLUBILITY(T) CSATW = SOLUBILITY(TW) F = FRICTION(RE,EPS,DIA) V = VELOCITY(FLOW,D,DIA) 149 V2 = V C Nucleated sodium sulphate p a r t i c l e s i z e [m] DIAPART = 2E-6 . C Q ****** * + *• + *•*'*•'* + *** * C Clean Pressure Drop £• * * * * * * * * * * * * * * * * * * * C DIACLEAN = 0.006272 VCLEAN1 = VELOCITY(FLOW,Dl,DIACLEAN) VCLEAN2 = VELOCITY(FLOW,D2,DIACLEAN) RECLEAN = REYN(FLOW,DIACLEAN,VISC) PRCLEAN = PRAN(VISC,CP,K) FCLEAN = FRICTION(RECLEAN,EPS,DIACLEAN) PRESS2 = PRESSURE(FCLEAN,DZ,FLOW,DIACLEAN,D,PRESS1,VCLEAN1, + VCLEAN2) FOULPRESS2 = PRESS2 C £ * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * C Pressure Drop Due To Density Change Q *********************************** C VDC1 = VELOCITY(FLOW,Dl,DIA) VDC2 = VELOCITY(FLOW,D2,DIA) AREA = PI*(DIA/2) **2 PDROP = FLOW*(VDC2-VDC1)/(AREA) PDROPTOT = PDROPTOT + PDROP C Q ******* C MODEL 1 Q ******* c IF (MODEL .EQ. 1) THEN C S a l t d e p o s i t i o n s t a r t s when wall s o l u b i l i t y l i m i t drops C below concentration of s o l u t i o n IF (CSATW .LE. C) THEN HM = TRANSMASS(TNUW,KW,DIA,DW,TLEW,CPW) IF (CSAT2 .GT. CB1) THEN C I f the s o l u b i l i t y l i m i t i s greater than the C s o l u t i o n concentration, the concentration C gradient f o r molecular d i f f u s i o n i s determined C by the actu a l s a l t s o l u t i o n concentration C (CB1) and the w a l l s o l u b i l i t y l i m i t (CSATW) FLOWMOL = RATEMASS(HM,DZ,DIA,DBB,CB1,CSATW) C Cal c u l a t e s the amount of d i s s o l v e d s a l t a f t e r molecular C t r a n s f e r CB2 = CDECREASE(CB1,FLOWMOL,FLOW) ELSE IF (CSAT2 . LE. CB.l) THEN C Cal c u l a t e s the amount of s a l t suspended as s o l i d s . C For the f i r s t s a l t d e p o s i t i o n step CBP1 w i l l C be 0. CBP2 = CBP1 + CB1 - CSAT2 C I f the s o l u b i l i t y l i m i t i s l e s s than the s o l u t i o n C concentration, i n t h i s model a l l s a l t above the C l i m i t p r e c i p i t a t e s out of s o l u t i o n ; therefore C the concentration gradient f o r d i f f u s i o n i s C determined by the d i s s o l v e d s a l t (CSAT2, which C i s the s o l u b i l i t y l i m i t ) and the wall s o l u b i l i t y C l i m i t (CSATW) FLOWMOL = RATEMASS(HM,DZ,DIA,DBB,CSAT2,CSATW) C Cal c u l a t e s the amount of s a l t l e f t a f t e r molecular C t r a n s f e r CB2 = CDECREASE(CSAT2,FLOWMOL,FLOW) END IF C FOUL c a l c u l a t e s the amount of s a l t deposited i n t h i s time C step. REMEMBER, the diameter (DIA) i s changing with C each time i n t e r v a l , so the surface area to deposit on C i s decreasing as the l a y e r gets t h i c k e r YSALT = FOULTHICK(FLOWMOL,DZ,DIA,DTIME,PHI) C Indexes the s a l t thickness, diameter and roughness f o r each C step length-wise. There may be some redundancy here. YTOT(ICOUNT) = YTOT(ICOUNT) + YSALT DIA = DIACLEAN - YTOT(ICOUNT)/500 EPSFOUL(ICOUNT) = EPS + YTOT(ICOUNT) C Recalculates Reynolds number with new roughness value f o r C the f r i c t i o n c o e f f i c i e n t and pressure drop c a l c u l a t i o n s REFOUL = REYN(FLOW,DIA,VISC) 150 FFOUL = FRICTION(REFOUL,EPSFOUL(ICOUNT),DIA) C Cal c u l a t e s the a c c e l e r a t i o n a l pressure drop V2 = VELOCITY(FLOW,D,DIA) . VPRESS = 0.5*D*(V2**2-V1**2) VPRESS2 = VPRESS2 + VPRESS DV = V2-V1 FOULPRESS2 = PRESSURE(FFOUL,DZ,FLOW,DIA,D,FOULPRESS1, + VI, V2 ) END IF END IF C Q ******* C MODEL 2 Q ******* C C The documentation f o r MODEL 2 i s s i m i l a r to MODEL 1 C except where noted. C IF (MODEL .EQ. 2) THEN IF (CSATW .LE. C) THEN HM = TRANSMASS (TNUW,KW, DIA, DW,TLEW,CPW) C A l l s a l t not deposited remains d i s s o l v e d so CB1 C i n t h i s case represents a l l s a l t l e f t i n the bulk, C and i s used i n determining the concentration gradient C f o r molecular d i f f u s i o n FLOWMOL = RATEMASS(HM,DZ,DIA,DBB,CB1,CSATW) CB2 = CDECREASE(CB1, FLOWMOL,FLOW) YSALT = FOULTHICK(FLOWMOL,DZ,DIA,DTIME,PHI) YTOT(ICOUNT) = YTOT(ICOUNT) + YSALT DIA = DIACLEAN - YTOT(ICOUNT)/500 EPSFOUL(ICOUNT) = EPS + YTOT(ICOUNT) REFOUL = REYN(FLOW,DIA,VISC) FFOUL = FRICTION(REFOUL,EPSFOUL(ICOUNT),DIA) V2 = VELOCITY(FLOW,D,DIA) VPRESS = 0.5*D*(V2**2-V1**2) VPRESS2 = VPRESS2 + VPRESS DV = V2-V1 F0ULPRESS2 = PRESSURE(FFOUL,DZ,FLOW,DIA,D,FOULPRESS1, + VI,V2) END IF END IF C Q ******* C MODEL 3 Q ******* C C Documentation for MODEL 3 i s s i m i l a r to MODEL 1 except C where noted C . IF (MODEL .EQ. 3) THEN C S a l t d e p o s i t i o n s t a r t s when bulk s o l u b i l i t y l i m i t drops C below concentration of s o l u t i o n IF (CSAT2 .LE. C) THEN IF (ICOUNT2 .EQ. 1) THEN C For the f i r s t s a l t dep. step i n which s a l t i s deposited C the i n i t a l concentration used f o r determining C the amount deposited w i l l be the s a l t s o l u t i o n C concentration (C). A f t e r that, the s a l t s o l u t i o n C w i l l always be at the s o l u b i l i t y l i m i t : CSAT2 f o r the C present length step, CSAT1 f o r the previous length step CSAT1 = C END IF C Ca l c u l a t e s the amount of s a l t deposited FLOWSALT = RATESALT(FLOW,CSAT1,CSAT2) YSALT = FOULTHICKfFLOWSALT,DZ,DIA,DTIME,PHI) YTOT(ICOUNT) = YTOT(ICOUNT) + YSALT DIA = DIACLEAN - YTOT(ICOUNT)/500 EPSFOUL(ICOUNT) • = EPS + YTOT(ICOUNT) REFOUL = REYN(FLOW,DIA,VISC) FFOUL = FRICTION(REFOUL,EPSFOUL(ICOUNT),DIA) V2 = VELOCITY)FLOW,D,DIA) VPRESS = 0.5*D*(V2**2-V1**2) VPRESS2 = VPRESS2 + VPRESS DV = V2-V1 FOULPRESS2 = PRESSURE(FFOUL,DZ,FLOW,DIA,D,FOULPRESS1, + VI,V2) 151 C Counter used here to eliminate use of above loop with the C statement CSAT1 = C a f t e r the f i r s t time ICOUNT2 = ICOUNT2 + 1 CB2 = CSAT2 END IF END IF C Q , ******* C MODEL 4 Q ******* C IF (MODEL .EQ. 4) THEN IF (CSATW .LE. C) THEN HM = TRANSMASS (TNUW, KW, DIA, DW, TLEW, CPW) IF (CSAT2 .GT. CB1) THEN FLOWMOL = RATEMASS(HM,DZ,DIA,DBB,CB1,CSATW) CB2 = CDECREASE(CB1,FLOWMOL,FLOW) ELSE IF (CSAT2 .LE. CB1) THEN C When the bulk s o l u b i l i t y l i m i t drops below the bulk C concentration, f o r t h i s model, both the d i s s o l v e d C and nucleated concentrations must be c a l c u l a t e d FLOWMOL = RATEMASS(HM,DZ,DIA,DBB,CSAT2,CSATW) CB2 = CDECREASE(CSAT2,FLOWMOL,FLOW) C Ca l c u l a t e s the amount of s a l t nucleated plus the C previous amount suspended. For the f i r s t s a l t C d e p o s i t i o n step, CBP1 w i l l be 0. CBP1B = CBP1 + CB1 '-• CSAT 2 C Deposition v e l o c i t y f o r suspended p a r t i c l e s C Deposition v e l o c i t y i s not an actual speed of the p a r t i c l e s C but a value that can be int e g r a t e d to determine a rate of C p a r t i c l e s d e p o s i t i n g on the i n s i d e wall C Taken from Papavegos et a l . (1984), which was an C summary of experimental data f o r d e p o s i t i o n i n C a h o r i z o n t a l flow system VISCKIN = VISCW/DW SC = VISCKIN/DIFFW DP = 2680 TAUW = D*V**2*F/8 USTAR = (TAUW/DW)**0.5 TAUP = DP*DIAPART**2/(18*VISCKIN*1E-6*DW) TAUPPLUS = TAUP*USTAR**2/(VISCKIN*lE-6) IF (TAUPPLUS .GT. 20) THEN VDSTAR =0.13 ELSE IF (TAUPPLUS .LT. 0.2) THEN , VDSTAR = 0.'065* (SC)** (-0.6667) ELSE VDSTAR =3.5E-4*TAUPPLUS**2 END IF VD = VDSTAR*USTAR CPBW = 0 C . C a l c u l a t e s mass d i f f u s i o n c o e f f i c i e n t f o r p a r t i c l e s FLOWPART = RATEMASS(VD,DZ,DIA,DBB,CBP1B,CPBW) C Cal c u l a t e s the present amount of suspended p a r t i c l e s C at the end of t h i s length step. CBP2 =-CDECREASE(CBP1B,FLOWPART,FLOW) END IF FLOWSALT = FLOWMOL + FLOWPART YSALT = FOULTHICK(FLOWSALT,DZ,DIA,DTIME,PHI) YTOT(ICOUNT) = YTOT(ICOUNT) + YSALT DIA = DIACLEAN-YTOT(ICOUNT)/500 EPSFOUL(ICOUNT) = EPS + YTOT(ICOUNT) REFOUL - REYN(FLOW,DIA,VISC) FFOUL = FRICTION(REFOUL,EPSFOUL(ICOUNT),DIA) V2 = VELOCITY(FLOW,D,DIA) VPRESS = 0.5*D*(V2**2-V1**2) VPRESS2 = VPRESS2 + VPRESS DV = V2-V1 FOULPRESS2 = PRESSURE(FFOUL,DZ,FLOW,DIA,D,FOULPRESS1, . + VI,V2) END IF END IF C SUPERSAT i s the r a t i o of d i s s o l v e d s a l t to the s o l u b i l i t y C l i m i t 'SUPERSAT = CB2/CSAT2 C • Q ************************* 152 C Outside Wall Temperature Q ************************* C RI = 0.003136 RO = 0.0048 IF (CSATW .LE. C) THEN TS = TW C The thermal c o n d u c t i v i t y of the s a l t l a y e r i s a C modelled l i k e many columns of stagnant water C and sodium sulphate i n p a r a l l e l . C PHI i s the p o r o s i t y f a c t o r which d i c t a t e s the C appropriate r a t i o of water to s a l t columns f o r C the thermal c o n d u c t i v i t y c a l c u l a t i o n KH20 = TCONDUCT(TS,P)/1000 KLAYER = KH20*PHI+KSALT*(1-PHI) C New i n s i d e radius to the s a l t l a y e r RS = DIA/2 C Re c a l c u l a t i n g the actu a l i n s i d e wall temperature C with the i n s i d e s a l t l a y e r surface temp. (TS) TW = TSALT(TS,Ql,KLAYER,RS) CTW = TW - 273.15 END IF K625 = TINCONELK(TW) Q2B = Ql/(3.14159265359*2*RO) C C a l c u l a t i n g the outside surface temperature using the C i n s i d e wall surface temperature as the o v e r a l l temp. C through the Inconel tube. TE = TWOUT(TW,Q2B,K625,RI,RO) CTE = TE - 273.15 TETW = TE - TW C Q ****************** C Output of Program Q ****************** C IF (TCOUNT2 .EQ. 1) THEN WRITE(7,100) 100 FORMAT('Z ','Tb ','Ts ','Tw ','Te ','SALT ','Cb * + 'Nuc ','Solub ','Sat ",'DP ','DPfoul ','HM ','MOL + 'VD ' , 'MASS ' , 'LE 1 ) END IF IF (TCOUNT3 .EQ. 10) THEN WRITE(7,200) Z,CT,CTS,CTW,CTE,YTOT(ICOUNT) + ,CB2,CBP2,CSAT2,SUPERSAT,PRESS2,FOULPRESS2, + HM,FLOWMOL,VD,FLOWPART,TLEW 200 FORMAT (F6.3, ' ',F8.3,' \F8.3,' ',F8.3,' ',F8.3,' ', + E15.6,' ',E15.6,' ',E15.6,' \E15.6,' ',E15.6,' ',E15.6, + E15.6,' ',E15.6,' ',E15.6,' ',E15.6,' ',E15.6,' ',E15.6) END IF C Q ******************** C Counters and Resets Q ******************** C Used to keep track of previous steps C DIA2(ICOUNT) = DIA EPSFOUL(ICOUNT) = EPS . PRESS1 = PRESS2 FOULPRESS1 = FOULPRESS2 CB1 = CB2 CBP1 = CBP2 CSAT1 = CSAT2 VI = V2 Z = Z + DZ ICOUNT = ICOUNT + 1 TCOUNT2 = TCOUNT2 + 1 Dl = D2 END DO TCOUNT = TCOUNT + DTIME TCOUNT3 = TCOUNT3 + 1 END DO 10000 CONTINUE END 153 Sample Input For SCHeatf Experimental Run 11 All inputs are prompted on the screen. ENTER THE HEAT FLUX [kW/m]: 5.581 ENTER THE MASS FLOW [kg/min]: 2.16 ENTER THE BULK TEMP [K]: 637.9 ENTER THE PRESSURE [MPa]: 25.08 ENTER THE LENGTH AND STEPSIZE [m] (separated by a comma) 3.1, 0.1 ENTER THE SALT DEPOSITION MODEL: 1. SUSPENDED PARTICLES 2. NO NULCEATION 3. CHAN ETAL. 4. COMPLETE 1 ENTER THE CONCENTRATION [wt%]: 1.066 ENTER THE FOULING TIME [s]: 63 154 Sample Output File From SCHeat.f Experimental Run 11 2 Tb Ts 0.1 366.443 377.854 0.2 368.059 378.752 0.3 369.598 379.623 0.4 371.058 380.452 0.5 372.437 381.239 0.6 373.733 381.981 0.7 374.943 382.658 0.8 376.065 383.267 0.9 377.097 383.833 1.0 378.038 384.351 1.1 378.891 384.797 1.2 379.658 385.234 1.3 380.345 385.649 1.4 380.957 386.112 1.5 381.501 386.606 1.6 381.985 387.123 1.7 382.42 387.644 1.8 382.814 388.159 1.9 383.173 388.658 2.0 383.503 389.153 2.1 383.806 389.651 2.2 384.085 390.143 2.3 384.343 390.62 2.4 384.583 391.093 2.5 384.81 391.578 2.6 385.027 392.058 2.7 385.238 392.546 2.8 385.449 393.047 2.9 385.662 393.564 3.0 385.883 394.148 Tw Te Ysalt 490.773 498.027 6.90E-01 508.697 515.828 7.78E-01 523.307 530.349 8.46E-01 534.09 541.069 8.93E-01 540.999 547.938 9.21 E-01 544.307 551.227 9.31 E-01 544.396 551.314 9.26E-01 541.918 548.851 9.10E-01 537.524 544.483 8.84E-01 532.375 539.363 8.55E-01 526.676 533.698 8.24E-01 520.882 527.939 7.91 E-01 513.67 520.771 7.52E-01 504.395 511.553 7.01 E-01 492.797 500.036 6.36E-01 480.956 488.284 5.68E-01 469.959 477.371 5.03E-01 460.154 467.643 4.44E-01 451.561 459.12 3.91 E-01 444.286 451.904 3.45E-01 438.108 445.777 3.05E-01 432.837 440.551 2.70E-01 428.323 436.075 2.39E-01 424.47 432.255 2.12E-01 421.189 429.003 1.89E-01 418.384 426.221 1.68E-01 416.003 423.862 1.50E-01 413.993 421.87 1.34E-01 412.311 420.202 1.20E-01 408.965 416.886 9.50E-O2 Cb Cbp Csat 1.03E+00 O.OOE+OO 1.87E+0O 9.87E-01 O.OOE+OO 1.68E+00 9.41 E-01 O.OOE+OO 1.51E+0O 8.90E-O1 O.OOE+OO 1.35E+00 8.37E-01 O.OOE+OO 1.21E+00 7.82E-01 O.OOE+OO 1.08E+00 7.28E-01 O.OOE+OO 9.68E-01 6.73E-01 O.OOE+OO 8.64E-01 6.20E-01 O.OOE+OO 7.71 E-01 5.68E-01 O.OOE+OO 6.89E-01 5.18E-01 O.OOE+OO 6.16E-01 4.71 E-01 O.OOE+OO 5.51 E-01 4.25E-01 O.OOE+OO 4.94E-01 3.81 E-01 O.OOE+OO 4.44E-01 3.40E-01 O.OOE+OO 4.01 E-01 3.02E-01 O.OOE+OO 3.62E-01 2.69E-01 O.OOE+OO 3.28E-01 2.39E-01 O.OOE+OO 2.97E-01 2.13E-01 O.OOE+OO 2.70E-01 1.90E-01 O.OOE+OO 2.44E-01 1.70E-01 O.OOE+OO 2.21 E-01 1.52E-01 O.OOE+OO 2.00E-O1 1.37E-01 O.OOE+OO 1.81 E-01 1.23E-01 O.OOE+OO 1.63E-01 1.10E-01 O.OOE+OO 1.46E-01 9.90E-02 O.OOE+OO 1.30E-01 8.91 E-02 O.OOE+OO 1.14E-01 8.03E-02 O.OOE+OO 9.89E-02 7.24E-02 O.OOE+OO 8.33E-02 5.89E-02 7.13E-03 6.53E-02 Supersaturation DP 5.49E-01 3.29E+02 5.87E-01 6.62E+02 6.23E-01 9.97E+02 6.58E-01 1.34E+03 6.91 E-01 1.68E+03 7.22E-01 2.03E+03 7.52E-01 2.38E+03 7.79E-01 2.73E+03 8.04E-01 3.09E+03 8.25E-01 3.45E+03 8.42E-01 3.82E+03 8.55E-01 4.19E+03 8.61 E-01 4.57E+03 8.58E-01 4.95E+03 8.48E-01 5.34E+03 8.35E-01 5.74E+03 8.20E-01 6.14E+03 8.05E-O1 6.56E+03 7.91 E-01 6.98E+03 7.79E-01 7.41 E+03 7.69E-01 7.85E+03 7.61 E-01 8.31 E+03 7.55E-01 8.77E+03 7.53E-01 9.24E+03 7.54E-01 9.73E+03 7.62E-01 1.02E+04 7.79E-01 1.07E+04 8.12E-01 1.13E+04 8.69E-01 1.18E+04 9.02E-01 1.24E+04 Dpfoul Hm Rate Mol. 1.01E+04 4.10E-03 1.31E-05 2.07E+04 4.45E-03 1.52E-05 3.43E+04 4.79E-03 1.69E-05 5.06E+04 5.07E-03 1.82E-05 6.89E+04 5.32E-03 1.91E-05 8.84E+04 5.51 E-03 1.96E-05 1.08E+05 5.66E-03 1.98E-05 1.27E+05 5.76E-03 1.96E-05 1.45E+05 5.84E-03 1.92E-05 1.62E+05 5.92E-03 1.86E-05 1.77E+05 5.98E-03 1.79E-05 1.91E+05 6.05E-03 1.72E-05 2.04E+05 6.08E-03 1.64E-05 2.15E+05 6.07E-03 1.59E-05 2.25E+05 6.00E-03 1.49E-05 2.33E+05 5.94E-03 1.35E-05 2.39E+05 5.88E-03 1.20E-O5 2.45E+05 5.83E-03 1.06E-O5 2.49E+05 5.80E-03 9.38E-06 2.53E+05 5.79E-03 8.25E-06 2.57E+05 5.79E-03 7.28E-06 2.60E+05 5.82E-03 6.43E-06 2.63E+05 5.85E-03 5.69E-06 2.66E+05 5.89E-03 5.05E-06 2.69E+05 5.95E-03 4.49E-06 2.71 E+05 6.01 E-03 3.99E-06 2.74E+05 6.08E-03 3.56E-06 2.76E+05 6.17E-03 3.18E-06 2.78E+05 6.26E-03 2.85E-06 2.80E+05 6.33E-03 2.29E-06 VD Rate Part. Lewis No. O.OOE+OO O.OOE+OO 2.03E+00 O.OOE+OO O.OOE+OO 1.86E+00 O.OOE+OO O.OOE+OO 1.68E+00 O.OOE+OO O.OOE+OO 1.52E+00 O.OOE+OO O.OOE+OO 1.36E+00 O.OOE+OO O.OOE+OO 1.21E+00 .i O.OOE+OO O.OOE+OO 1.07E+00 It O.OOE+OO O.OOE+OO 9.47E-01 O.OOE+OO O.OOE+OO 8.39E-01 O.OOE+OO O.OOE+OO 7.45E-01 O.OOE+OO O.OOE+OO 6.68E-01 O.OOE+OO O.OOE+OO 6.04E-01 O.OOE+OO O.OOE+OO 5.55E-01 O.OOE+OO O.OOE+OO 5.19E-01 O.OOE+OO O.OOE+OO 4.96E-01 O.OOE+OO O.OOE+OO 4.85E-01 O.OOE+OO O.OOE+OO 4.82E-01 O.OOE+OO O.OOE+OO 4.84E-01 O.OOE+OO O.OOE+OO 4.90E-01 O.OOE+OO O.OOE+OO 4.99E-01 O.OOE+OO O.OOE+OO 5.12E-01 O.OOE+OO O.OOE+OO 5.26E-01 O.OOE+OO O.OOE'UO 5.43E-01 O.OOE+OO O.OOE+OO 5.61 E-01 O.OOE+OO O.OOE+OO 5.81 E-01 O.OOE+OO O.OOE+OO 6.01 E-01 O.OOE+OO O.OOE+OO 6.23E-01 O.OOE+OO O.OOE+OO 6.45E-01 O.OOE+OO O.OOE+OO 6.67E-01 O.OOE+OO O.OOE+OO 6.89E-01 Computer Program Salt. Q ******************************************************************** PROGRAM SALT Q ********************************************************* C Convering outside surface tube temperatures to s a l t thicknesses Q ******************************************************************** C Q ************************* C Declaration of Va r i a b l e s Q ************************* C C C = the concentration of the s a l t i n the f l u i d [wt%] C CP = s p e c i f i c heat [kJ/kg-K] C CPW = using wall temp, pr o p e r t i e s [kJ/kg-K] C D = de n s i t y of flow [kg/m~3] C DH = d i f f e r e n c e i n enthalpies between step s i z e s [kJ/kg] C DIA = diameter of the tube [m] C DIFTE = d i f f e r e n c e between measured and c a l c u l a t e d [K] C outside wall temperature C DTE = d i f f e r e n c e between TE and TE2 [K] C DTWTB = the d i f f e r e n c e between TWTB2 and TWTB used f o r [K] C i t e r a t i o n f o r convergence of TWTB C DW = de n s i t y of f l u i d at i n s i d e wall temperature [kg/m~3] C ' DZ = s t e p s i z e along the tube length [m] C FLOW = massflow [kg/s] C FL0W2 = massflow [kg/min] C HI = enthalpy of previous step [kJ/kg] C H2 = enthalpy of present step [kJ/kg] C HM = mass t r a n s f e r c o e f f i c i e n t [m/s] C HW = enthalpy at wall temperature [kJ/kg] C ICOUNT = counter f o r a x i a l l o c a t i o n [-) C IC0UNT2 = counter f o r inputing outside temperatures [-] C IFLAG = tracks i f there i s a no thermocouple reading (-] C f o r that a x i a l p o s i t i o n C K = thermal c o n d u c t i v i t y [mW/K-m] C K625 = thermal c o n d u c t i v i t y of Inconel 625 at TK [W/K-m] C KH20 = thermal c o n d u c t i v i t y of water i n pores [W/K-m] C i n s a l t l a y e r C KSALT = thermal c o n d u c t i v i t y of Na2S04 determined [W/K-m] C by mass balance C KLAYER = e f f e c t i v e thermal c o n d u c t i v i t y of s a l t [W/K-m] C la y e r C KW = using wall temp, pr o p e r t i e s [mW/K-m] C PHI = the p o r o s i t y value f o r the s a l t l a y e r [%] C PR = Prandtl number [-] C PRW = using wall temp, pr o p e r t i e s [-] C Ql = heat input per un i t length of tube [kW/m] C Q2 = heat input per un i t area of tube [kW/mA2] C RE = the Reynolds number of the flow [-] C REW = using wall temp, pr o p e r i t e s [-] C RI = i n s i d e radius of the tube [m] C RO = outside radius of the tube [m] C RS = i n s i d e radius of the s a l t d e p o s i t i o n [m] C RUN = the experimental run number [-] C T = temperature [K] C TCHECK = used to f i n d T2 with H2 [K] C TE = external wall temperature [K] C TE2 = r e c a l c u l a t i o n of external wall temperature [K] C TNU = Nusselt number [-] C TNUW = using wall temp, pr o p e r t i e s [-] C TS = surface temperature under the l a y e r of s a l t [K] C TW = i n s i d e wall temperature [K] C TW2 = c a l c u l a t e d using TWTB2 (using wall temp, property [K] C v a r i a t i o n s C TWTB = TW - TB, d i f f e r e n c e between wall and bulk temp. [K] C TWTB2 = using wall temp, property v a r i a t i o n s [K] C VISC = v i s c o s i t y [mg/s-m] C VISCW = using wall temp, prop e r t i e s [mg/s-m] 156 YSALT = thickness of s a l t d e p o s i t i o n on tube walls [m] YSALT2 = thickness of s a l t deposit (mm] Z = distance along the tube length [m] Functions c a l c u l a t e s new enthalpy Prandtl number Reynolds number thermal c o n d u c t i v i t y of water thermal c o n d u c t i v i t y of Inconel Lewis number uses Swenson/Carver c o r r e l a t i o n c a l c u l a t e s temperature through s a l t l a y e r c a l c u l a t e s Tw - Tb outside wall temperature v i s c o s i t y of water ENTHALPY(HI,Ql,DX,FLOW) PRAN(VISC,CP,K) REYN(FLOW,DIA,VISC) TCONDUCT(T,P) TINCONELK(TK) TLEWIS(K,D,CP,DIFF) TNUS1 (RE, PR, DBB, DW) TSALT(TS,Ql,KLAYER,RS) TWTBFUN(Q2,DIA,TNU,K) TWOUT(TW,Q2,K625,RI,RO) VISCOSITY(T,P) IMPLICIT REAL*8 (A-H,K-M,O-Z) IMPLICIT INTEGER (I,J,N) DIMENSION TE(30) DIMENSION Z(30) DIMENSION TE2(30) C C ******************************************************** C The fo l l o w i n g 'COMMON' statements were included from the C EQTEST.F main program Q ***************************************************** C COMMON/CCPEQ/TCEQ,PCEQ,DCEQ COMMON/CSUB2/R,XMOL,TC,PC,DC COMMON/CNORM/TNORM,DNORM COMMON/CSUB3/TTR,PTR,DLTR,DVTR,TBOYL,PBOYL,DLB,DVB COMMON/COUT/NIN,NOUT INPUT / OUTPUT ON PC: NIN = 5 NOUT = 6 *********** INPUT DATA WRITE (NOUT, 1001) 1001 FORMAT(/,' ENTER THE HEAT FLUX [kW/m]:') READ (NIN,*) Ql WRITE (NOUT, 1002) 1002 FORMAT!/,' ENTER THE MASS FLOW [kg/min]:') READ (NIN,*) FLOW2 WRITE (NOUT, 1003) 1003 FORMAT!/,' ENTER THE BULK TEMP [K]:') READ (NIN,*) T WRITE (NOUT, 1004) 1004 FORMAT!/,' ENTER THE PRESSURE [MPa]:') . READ (NIN,*) P WRITE (NOUT, 1005) 1005 FORMAT!/,' ENTER THE SURFACE TEMPERATURES [K]:') READ (NIN, *) TE(1),TE(2),TE(3),TE(4),.TE(5),TE(6),TE(7) +,TE(8),TE(9),TE(10),TE(11),TE(12),TE(13),TE(14), +TE(15),TE(16) KSALT =5.8 PHI = 0.71 DIA = 0.006272 Q2 = Ql/(3.14159265359*DIA) FLOW = FLOW2/60 ****************************** C C C Opening F i l e f o r Data Storage Q ****************************** C OPEN (UNIT=7, FILE="Saltl.txt') C Q *********************** C Constants and Counters 157 * + * + + + + + + + * * * + * * * * * + *•** Z ( l ) = o. Z(2) = 0.063 Z(3) = 0.209 Z(4) = 0.35 Z(5) = 0.496 Z(6) = 0.715 Z(7) = 0.853 Z(8) = 1.024 Z(9) = 1.218 Z(10) = 1.407 Z ( l l ) = 1.551 Z(12) = 1.897 Z(13) = 2.278 Z(14) = 2.414 Z(15) = 2.551 Z(16) = 2.69 Z(17) = 2.822 PI = 3.1415926535 YSALT " 0 ICOUNT = 2 I FLAG = 1 * * * * * * * * * * * * * * * * * * * I n i t i a l Conditions ******************* DO WHILE (ICOUNT .LE. 17) DS = BDENS(T,P,0) D = DENS (P,T,DS, l.D-6) HI = HB (T, D) VISC = VISCOSITY(T,P) K = TCONDUCT(T, P) CP = CPB(T,D) RE = REYN(FLOW,DIA,VISC) PR = PRAN(VISC,CP,K) DZ = Z(ICOUNT) - Z(ICOUNT-l) H2 = ENTHALPY(HI,Ql,DZ,FLOW) CP = CPB(T,D) DH = H2 - HI DH2 = = DH TCHECK = T Loop to i t e r a t e to f i n d the temperature at the new enthalpy DO WHILE (DH2 .GT. 0.001) TCHECK = TCHECK + DH/CP DS = BDENS(TCHECK,P,0) D = DENS(P,TCHECK,DS, l.D-6) CP = CPB(TCHECK,D) HI = HB(TCHECK,D) DH = H2 - HI DH2 = ((DH)**2)**0.5 END DO T = TCHECK CT = T - 273.15 HI = H2 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * R e c a l c u l a t i o n of pr o p e r t i e s at new T ************************************* DW = D VISC = VISCOSITY(T,P) K = TCONDUCT(T, P) CONTINUE DIA = 0.006272 - 2*YSALT RE = REYN(FLOW,DIA,VISC) PR = PRAN(VISC,CP,K) TNU = TNUS1 (RE,PR,D,DW) TWTB = TWTBFUN(Ql,TNU,K) * * * * * * * * * * * * * * * * Wall Properties 158 Q **************** C 10 CONTINUE TW = T + TWTB DSW = BDENS(TW,P,0) DW = DENS(P,TW,DSW,l.D-6) HW = HB(TW,DW) CPW = CPB(TW,DW) KW = TCONDUCT(TW,P) VISCW = VISCOSITY(TW,P) REW = REYN(FLOW,DIA,VISCW) PRW = (HW-H2)/TWTB*VISCW/KW TNUW = TNUS1(REW,PRW,D,DW) TWTB2 = TWTBFUN(Ql,TNUW,K) TW2 = T + TWTB2 ******************** C C C Convergence of TWTB C ********************** C DTWTB1 = ((TWTB2 - TWTB)**2)**0.5 IF (DTWTB1 .GT. 0.01) THEN TWTB = TWTB2 GOTO 10 END IF 11 CONTINUE C Q ************************ C Outside Wall Temperature C + + + + + + C DTE = 1 TS = TW CTS = TS - 273.15 RI .= 0.003136 RO = 0.0048 KH20 = TCONDUCTITW,PJ/1000 KLAYER = (PHI)*KH20+(1-PHI)*KSALT Q2B = Ql/(3.14159265359*2*RO) IF (IFLAG .EQ. 2) THEN RS = DIA/2 TW => TSALT(TS,Q1, KLAYER, RS) END IF K625 = TINCONELK(TW) TE2(ICOUNT-l). = TWOUT(TW,Q2B,K625,RI,RO) CTW = TW - 27 3.15 C Q ************************************ C Outside Wall Temperature Comparison Q ************************************ C IF (TE(ICOUNT-l) .LT. 274) THEN CTS = 0 CTW = 0 CTE = 0 GOTO 20 END IF DIFTE = TE(ICOUNT-l) - TE2(ICOUNT-1) DIFTE2 = ((TE(ICOUNT-1) - TE2(ICOUNT-1))**2)**0.5 IF (DIFTE2 .GT. 0.1) THEN I FLAG = 2 YSALT = YSALT + DIFTE/1000000 GOTO 30 END IF CTE = TE2(ICOUNT-1) - 273.15 20 CONTINUE C Q ******************* C Write Data To F i l e C ******************* C IF (ICOUNT .EQ. 2) THEN WRITE(7,100) 100 FORMAT('"Z","TBULK [C]", nTSALT [C]","TWALLin +[C]"TWALLout","SALT THICKNESS [mm]"') END IF YSALT2 = YSALT*1000 159 WRITE(7,200) Z{ICOUNT),CT,CTS,CTW,CTE,YSALT2 200 FORMAT (F6.3, ' ' ,F8.3," ',F8.3,' ',F8.3, ' ',F8.3,' ',E15.6) C Q + + •*• + *•*** + + + + + + + * + + ** C Counters and Resets Q ** + ****•*•**•*• + •*•**• + **** c ICOUNT = ICOUNT + 1 I FLAG «- 1 END DO END 160 Sample Input For Salt.f Experimental Run 11 All inputs are prompted on the screen. ENTER THE HEAT FLUX [kW/m]: 5.581 ENTER THE MASS FLOW [kg/min]: 2.16 ENTER THE BULK TEMP [K]: 637.9 ENTER THE PRESSURE [MPA]: 25.08 ENTER THE SURFACE TEMPERATURES [K]: 663.45 702.55 721.15 735.65 783.75 841.45 888.05 901.75 907.65 878.45 845.05 795.85 778.55 762.65 273.15 Enter 0 °C or 273.15 K for bad thermocouple 736.35 161 Sample Output File From Salt.f Experimental Run 11 z Tb Ts Tw Te Ysalt 0.063 365.825 378.039 382.037 390.214 2.75E-02 0.209 368.201 378.895 421.497 429.308 2.80E-01 0.35 370.338 379.935 440.253 447.905 3.87E-01 0.496 372.383 380.962 454.872 462.404 4.66E-01 0.715 375.117 381.999 503.336 510.5 7.26E-01 0.853 376.623 382.445 561.385 568.207 1.01E+00 1.024 378.25 383.102 608.425 614.993 1.21E+00 1.218 379.788 383.98 622.196 628.692 1.26E+00 1.407 380.997 384.684 628.109 634.576 1.28E+00 1.551 381.755 385.34 598.779 605.397 1.15E+00 1.897 383.163 386.641 565.194 571.995 9.93E-01 2.278 384.288 388.249 515.697 522.785 7.43E-01 2.414 384.616 388.838 498.294 505.492 6.49E-01 2.551 384.921 389.427 482.265 489.582 5.58E-01 2.69 385.217 Bad Thermocouple 2.822 385.495 390.627 455.768 463.293 4.01 E-01 162 £91 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 3 (2A 'TA'tssayd'a'via'M0^'za'£)aunssaad NoixoNna SVIVSH 0.N3 aa = mraa M/0SIA»d3 = Hd (z-v) 8*iV3y u o n a w i O j ' a o ' o s i A l N v y a N O I I O N P U 8VTV3H + + + + ** + * * * * * * + * * * + * * * * * j f * + **jf* + * * + * + * + + + * * * + + * + * * * + + * * * + * * * + + * + * + ** + -»D CIN3 Nanxan XTYSA = MOIHXIflOJ 3WIXa*009e*((IHd-T)*89-3*wia»Id*Za)/ilVSMOli = XTtfSA •una U T S T » 3 I H X i n 0 3 -s^a3(Ood 3 ja^e« u . } X M JaAex 3 i e s aq} J O J A:+xsuap aBejaAB ue auxuna^ap 3 oq. (IHd) JOioej Aixsojod aq} sa^ejodjooux u o x } e x n o I E O ssau^oxqj, 3 69 £ S 9 3 6 S T H - £ = Id ( Z - V I 8*Ttf3a XlOI/IdWI (iHd'swixa'via'za'iTtfSMOidlMoiHnnoa N O I X D N O J 8*TV3>I aN3 NHHX3M J = NOIXDIHi (TT*T*»( (000T*Via»i. -C)/Sd3)+3a/6-9)0TSOl*8'I) = J (z-v) 8*ivaa xiondwi + + + + + + + + + * + + + + + + + + + + + + * + * + * + + + + *** + ***4-* + + ** + + + * + * + ****** + + + * + *** + + *+D (Via'Sda'SHlNOIXOIHJ N0IIDNO3 8*TO3H 0N3 NHnxaa 2H = AdTYHXN3 MOIi/ZCUlO + IH = 2H (z-v) 8»iV3H xionawi * + + ** + * + + + + * + * + + + * + + ** + *** + #jf- + 4**** + + jf* + ***^ + ** + * + * + *** + * + + * + * + + + * + + *0 (MOTH ' ZQ ' TO' TH)AdTYHXNS NOIIONfLI 8»TV3S aN3 N^nxaa i i i a = asrujia (9-3T»TOWViatMDSIA*Id*C)/MX^ZXIOO = 331a i.2S000000000-o = ic-wvia uox^Bnba U T 3 ^ S U T 3 - S S > ( O ^ S pue [s/ZJn] 0 L-392"0 lenba (L66T ) ' I S i s sap°H ux pasn a n x B A AiXAXsnijxp 3 aq} q ^ X M paq.Buix}sa s e « aq . s q d x n s uinxpos j o jra^auiBxp j e x n o a x o u i aqj , 3 ez-38e -i = z x i o a 69C59Z65I t 'T"£ = Id (z-v) s*Ttf3H n o n a m ( M D S I A ' M X ) 3S033ia NOIXONOa 8»Ttf3H 0N3 Nanxaa ZHO = 3SY3M33CI3 001 » M013/"I0WMO13 - 133 = 230 s x a p o u i a q i j o sq.uauoduioo a x o x ^ j s d papuadsns 3 pus paAiossxp q^oq J O J ' 3 - j a x }T E S J ° l u n o u i s a q . B x n o x B O 03 p a s n 0 (Z-V) 8*TW3H XlOIldWI »3 (M01d'TOWM013'XaO)3SV3H03aO N0IX0NO3 8*TV3H 0 SN0II3NO3 D + + + * + + * + + + + + + + + + * + + + + + + + + + + * + + + * + + + + + * + +3 j-;iBs PUB J*;B3H3S JOJ suoipanjf IMPLICIT REAL*8 (A-Z) PI = 3.14159265359 C Pressure drop equation subtracts the a c c e l e r a t i o n a l pressure drop C that would not be measured by the DP c e l l s i n the experimental C system. Therefore we can compare the models pre d i c t e d pressure C drop with the data PRESS = F*DZ*FLOW**2<'8/ (DIA**5*PI**2*D)+PRESS1-0. 5*D* (V2**2-V1**2 ) PRESSURE = PRESS RETURN END Q********************************************************************* REAL*8 FUNCTION RATEMASS(HM,DZ,DIA,DBB,CSAT2,CSATW) Q******************************************************* ************** IMPLICIT REAL*8 (A-Z) PI = 3.14159265359 C Used f o r MODELS 1,2 and 4 f o r molecular and mass d i f f u s i o n c o e f f . C For the mass d i f f u s i o n c o e f f . , HM i s replaced by VD (deposition C v e l o c i t y ) FLOWMOL = HM*DZ*PI*DIA*DBB*(CSAT2-CSATW)/100 RATEMASS = FLOWMOL RETURN END c********************************************************************* REAL*8 FUNCTION RATESALT(FLOW,CSAT1,CSAT2) c*************** + * * * * * * * * ^ IMPLICIT REAL*8 (A-Z) C Used f o r MODEL 3, immediate de p o s i t i o n of a l l p a r t i c l e s above C the s o l u b i l i t y l i m i t FLOWSALT = FLOW*(CSAT1-CSAT2)/100 RATESALT = FLOWSALT RETURN END REAL*8 FUNCTION REYN(FLOW,DIA,VISC) IMPLICIT REAL*8 (A-Z) PI = 3.14159265359 RE = 4*FL0W/(PI*DIA*VISC)*1000000 REYN = RE RETURN END REAL*8 FUNCTION SOLUBILITY(T) Q********************************************************************* IMPLICIT REAL*8 (A-Z) T2 = T - 273.15 C Experimentally determined s o l u b i l i t y equation IF (T2 .LT. 385.8) THEN CSAT = -LOG((T2-337.706021/49.11281)*3.49612 ELSE IF (T2 .GT. 388.5) THEN CSAT = 2.2/((T2-385.645)*LOG(1000*T2**1.2)*32.19) ELSE CSAT = 10**(232.3458-0.6051S6*T2) END IF SOLUBILITY = CSAT RETURN END REAL*8 FUNCTION TCONDUCT(T,P) IMPLICIT REAL*8 (A-Z) TT = T-273.15 IF (P .LT. 25) THEN IF (TT .LT. 25) THEN KI = 573.4 + (TT-0)/25*(617.3-573.4) ELSE IF (TT .LT. 50) THEN KI = 617.3 + (TT-251/25*(654-617.3) ELSE IF (TT .LT. 75) THEN KI = 654 + (TT-501/25*(678-654) ELSE IF (TT .LT. 100) THEN' KI = 678 + (TT-75)/25*(691.3-678) ELSE IF (TT .LT. 150) THEN KI = 691.3 + (TT-100)/50*(696.8-691.3) ELSE IF (TT .LT. 200) THEN KI = 696.8 + (TT-150)/50*(681.2-696.8) ELSE IF (TT- .LT. 250) THEN KI = 681.2 + (TT-200)/50*(643.6-681.2) 164 ELSE IF (TT .LT. 300) THEN KI = 643 .6 + (TT-250J/50* (576 .2-643 .6) ELSE IF (TT .LT. 350) THEN KI = 576 .2 + (TT-300)/50* (472 .8-576 .2) ELSE IF (TT .LT. 37 5) THEN KI = 472 .8 + (TT-350)/25* (441 . 5-472 .8) ELSE IF (TT .LT. 4 00) THEN KI = 441 .5 + (TT-375)/25* (128 .6-441 .5) ELSE IF (TT .LT. 425) THEN KI = 128 .6 + (TT-4001/25* (107 .1- 128 .6) ELSE IF (TT .LT. 450) THEN KI = 107 .1 + (TT-4251/25* (99. 01- 107 .1) ELSE IF (TT .LT. 475) THEN KI = 99. 01 + (TT-450)/25* (95. 70- 99. 01) ELSE IF (TT .LT. 500) THEN KI = 95. 70 + (TT-4751/25* ( 94 . 75- 95. 70) ELSE IF (TT .LT. 550) THEN KI = 94 . 75 + (TT-5001/50* (96. 51- 94 . 75) ELSE IF (TT .LT. 600) THEN KI = 96. 51 + (TT-5501/50* (100 .7- 96. 51) ELSE IF (TT .LT. 650) THEN KI = 100 .7 + (TT-600)/50* (106 -100.7) ELSE IF (TT .LT. 700) THEN KI = 106 + (TT-6501/50*(111.8 -106) ELSE IF (TT .LT. 750) THEN KI = 111 .8 + (TT-7001/50* (117 .7- I l l .8) ELSE IF (TT .GE. 750) THEN KI = 117 .7 + (TT-750)/50* (123 .5-117 .7) END IF END IF IF (TT . LT. 25) THEN K2 = 574 8 + (TT-01/25*(618.5- 574.8) ELSE IF (TT LT. 50) THEN K2 = 618 5 +• (TT-25)/25*(655.1 618.5) ELSE IF (TT LT. 75) THEN K2 ' = 655 1 + (TT-50)/25*(679.2 655.1) ELSE IF (TT LT. 100) THEN K2 = 679 2 + (TT-751/25*(692.7 67 9.2) ELSE IF (TT LT. 150) THEN K2 = 692 7 + (TT-100)/50* (698. 4 -692 7) ELSE IF (TT LT. 200) THEN K2 = 698 4 + (TT-1501/50* (683. 2 -698 4) ELSE IF (TT LT. 250) THEN K2 = 683 2 + (TT-2001/50* (646. 3 -683 2) ELSE IF (TT LT. 300) THEN K2 = 646 3 + (TT-2501/50* (580. 7 -646. 3) ELSE IF (TT LT. 350) THEN K2 = 580 7 + (TT-300)/50* (481. 4 -580 7) ELSE IF (TT LT. 375) THEN K2 = 481 4 + (TT-350)/25* (411. 4 -481 4) ELSE IF (TT LT. 4 00) THEN K2 = 411 4 + (TT-3751/25* (169. 3 -411 4) ELSE IF (TT LT. 4 25) THEN K2 •= 169 3 + (TT-4001/25* (123. 2 -169. 3) ELSE IF (TT LT. 450) THEN K2 = 123 2 + (TT-425)/25* (108. 8 -123. 2) ELSE IF (TT LT. 475) THEN K2 = 108 8 + (TT-4501/25* (102. 7 -108. 8) ELSE IF (TT LT. 500) THEN K2 = 102 7 + (TT-475)/25* (100. 3 -102. 7) ELSE IF (TT LT. 550) THEN K2 = 100 3 + (TT-5001/50* (100.6 -100. 3) ELSE IF (TT LT. 600) THEN K2 = 100 6 + (TT-5501/50* (104 . 1 -100 6) ELSE IF (TT LT. 650) THEN K2 = 104 1 + (TT-6001/50* (109. 1 -104 1) ELSE IF (TT LT. 700) THEN K2 = 109 1 + (TT-650J/50* (114 . 6 -109 1) ELSE IF (TT LT. 750) THEN K2 = 114 6 + (TT-7001/50* (120. 3 -114 6) ELSE IF (TT GE. 750) THEN K2 = 120 .3 + (TT-750J/50* (126. 0 -120 3) END IF IF (P .GT. 25) THEN IF (TT .LT. 25) THEN K3 = 576.1 + (TT-0)/25*(619.6-576.1) ELSE IF (TT .LT. 50) THEN 165 K3 = 619.6 + (TT-25)/25*(656.3-619.6) ELSE IF (TT .LT. 75) THEN K3 = 656.3 + (TT-50)/25*(680.4-656.3) ELSE IF (TT .LT. 100) THEN K3 = 680.4 + (TT-75)/25*(694-680.4) ELSE IF (TT .LT. 150) THEN K3 = 694 + (TT-100)/50*(700.1-694) ELSE IF (TT .LT. 200) THEN K3 = 700.1 + (TT-150)/50*(685.3-700.1) ELSE IF (TT .LT. 250) THEN K3 = 685.3 + (TT-2001/50*(649.1-685.3) ELSE IF (TT .LT. 300) THEN K3 = 649.1 + (TT-250)/50*(585-649.1) ELSE IF (TT .LT. 350) THEN K3 = 585 + (TT-300)/50*(489.1-585) ELSE IF (TT .LT. 375) THEN K3 = 489.1 + (TT-350)/25*(425.8-489.1) ELSE IF (TT .LT. 400) THEN K3 = 425.8 + (TT-375)/25*(249.1-425.8) ELSE IF (TT .LT. 425) THEN K3 = 249.1 + (TT-4001/25*(145.5-249.1) ELSE IF (TT .LT. 450) THEN K3 = 145.5 + (TT-4251/25*(121-145.5) ELSE IF (TT .LT. 475) THEN K3 = 121 + (TT-450)/25*(lll-121) ELSE IF (TT .LT. 500) THEN K3 = 111 + (TT-475)/25*(106.6-111) ELSE IF (TT .LT. 550) THEN K3 = 106.6 + (TT-500)/50*(10S-106.6) ELSE IF (TT .LT. 600) THEN K3 = 105 + (TT-550)/50*(107.8-105) ELSE IF (TT .LT. 650) THEN K3 = 107.8 + (TT-600)/50*(112.4-107.8) ELSE IF (TT .LT. 700) THEN K3 = 112.4 + (TT-650)/50*(117.6-112.4) ELSE IF (TT .LT. 750) THEN K3 = 117.6 + (TT-7001/50*(123.1-117.6) ELSE IF (TT .GE. 750) THEN K3 = 123.1 + (TT-750)/50*(128.6-123.1) END IF END IF IF (P .LT. 25) THEN K = Kl + (P-22.5)/2.5*(K2-K1) END IF IF (P .GT. 25) THEN K = K2 + (P-25)/2.5*(K3-K2) END IF IF (P .EQ. 25) THEN K = K2 END IF TCONDUCT = K RETURN END Q******************************************************************** REAL*8 FUNCTION TINCONELK(TK) Q***** *************************************** + *** + ******************* IMPLICIT REAL*8 (A-Z) TK2 = TK - 273.15 IF (TK2 .LT. 100) THEN K625 = (TK2-23)/(100-23)*(ll.4-9.81+9.8 ELSE IF (TK2 .LT. 200) THEN K625 = (TK2-100)/(200-100)*(13.4-11.4)+11.4 ELSE IF (TK2 .LT. 300) THEN K625 = (TK2-200)/(300-200)*(15.5-13.4)+13.4 ELSE IF (TK2 .LT. 400) THEN K625 = (TK2-300)/(400-300)*(17.6-15.51+15.5 ELSE IF (TK2 .LT. 500) THEN K625 = (TK2-400)/(500-400)*(19.6-17.61+17.6 ELSE IF (TK2 .LT. 600) THEN K625 = (TK2-500)/(600-500)*(21.3-19.61+19.6 ELSE IF (TK2 .GE. 600) THEN K625 = (TK2-6001/100*(21.3-19.6)+21.3 END IF TINCONELK = K625 RETURN END Q************* ******************************************************** 166 L91 N3HI (09T ' I T XX) 31 3S13 <9-fr8e-6-882)*92/(9£.-II) + 9-t>8€ = 20SIA N3HI (OOT "XT XX) 31 3S13 (e'T99-9'fr8e)*9Z/(09-II) + e'T99 = 20SIA N3HX (9i. "XT XX) 31 3S13 {8"988-C"T99)*9Z/(SZ-XX) + 8'988 = Z3SIA . N3HX (09 "IT XI) 31 3S13 (6eLT-8-988 )»93/(0-II) + 6£LT = 23SIA N3HI (92 ' I T IX) 31 ST'Ci.2- I = II (Z-V) 8*TV3a ii o n a w i ******** ,**» ,********»***» ,************************** ,* ,************»0 (d'I)AIISCOSIA NOIXONOi 8*TV3H ************** *************************»*****************************D (3N3 NHC1I3H 13A » AII0013A (Z**(3/VId) *Id*a) /M013 = 13A 6ses9Z6gTfrT-£ = id (Z-V) 8*TV3y HOIldWI ********,***»*************************»**********»**********»*»*****0 (VIQ"a'M013)AII0013A N0II3Nn3 8*TV3H ** , •» ,* • •* • •**»**•*» ,»*******»******»*****»*************************D aN3 NMfllSM SIMI = N03HIMI ooooooT»(69eg9Z6gT*T:e*N*nNi)/TO = aiMi (z-v) 8 *T Y 3 M xioiidwi ********************************************************* + + + + ******* *D (M'nNl'lOlNOHaXMI NOIIDNfU 8*TV3H ******************************************************************** *D aN3 NHnisa 31 = inOMI ((2**V-T)/(T-(2**V)901-2.*V))*(929>l*2)/IH*000T*ZO + MI = 31 U O T I . B J 3U 3 6 aeau; U I T M T T e M J O J uoT^enba uoxionpuoo xeuijam 3 oa/iy = V (z-v) 8*TV3y i i o i idwi **************************************************+***********+*****D (Oa'ia'SS9>l'20'MI)inOMX NOIIDNftJ 8VTV3H *******************,******************»**********»******************D aN3 Nyni3H MI = ITVSI (SM/iy)901*(H3AVTH*Id*Z)/000T*TO + SI = MI 9cxcoo'o = m 6SeS9Z6STfrT"€ = Id (z-v) 8*Ttf3a i i o n a w i ********************************************************************D (SH'MSAVTM'IO'SI)ITVSI N0IIDNO3 8*TV3H ********************,***********************************************D aN3 N^nisa WH = SSVWSMV I^ (i.8£'0**M31I*MdD*Via*Ma)/9-3T*MM*MnNI = WH (Z-V) 8VTV3H IIDIldWI *********************************************************************0 (MdO'M31X'Ma'Via'MM'MnNX)SSVWSNVHI NOIIONft-l 8*1Y3H ***•*"***., *•*•*******•**»**•***••****••»•****,************************0 aN3 Nynisy DNI = TSflNI TE2'0** (93Q/Ma)*£T9'0 ** (MMd)*£Z6'0** (M3H) *69fr00 ' 0 = (INI •ou '[5PU B Jd spTouAay 0 J O J saxq.jado.id T T E R T 3 s n pinoqs uox*eia:r:roo • xe +a uosuawg o (Z-V) 8*TV3H HOIldWI ***************************************,»****************************D (Ma'aaa'MHd'M3H)TSnNI N0II0NO3 8*1Y3H *********************************************************************D aN3 Nynisa 311 = SIM31I (M33IQ*MdD*MQ)/9-3T*MM = 311 uoxqenba u x a q s u T 3 - s a 3 ( o : } s UIOJJ pauxuua+ap quaxoxjiaoo uoTsnijTp sasn 3 (Z-V) 8*TV3H HOIldWI *********************************************************************3 (M33ia'Md3'MCTM>0SIM31I N0II0NO3 8*TV3y .LT. 375 72.71 + .LT. 4 00 58.09 + .LT. 425 29.00 + .LT. 450 28.89 + .LT. 500 29.70 + .LT. 550 30.61 + .LT. 600 34.50 + .LT. 7 00 36.45 + .LT. 750 38.38 + .GE. 750 40.26 + VISC2 = 288.9 + ELSE IF (TT .LT. 200 VISC2 = 188.2 + ELSE IF (TT .LT. 250 VISC2 = 139.3 + ELSE IF (TT .LT. 300 VISC2 = 111.4 + ELSE IF (TT .LT. 350 VISC2 = 91.67 + ELSE IF (TT VISC2 = ELSE IF (TT VISC2 = ELSE IF (TT VISC2 = ELSE IF (TT VISC2 = 28.36 + ELSE IF (TT .LT. 475 VISC2 = ELSE IF (TT VISC2 = ELSE IF (TT VISC2 = ELSE IF (TT VISC2 = 32.54 + ELSE IF (TT .LT. 650 VISC2 = ELSE IF (TT VISC2 = ELSE IF (TT VISC? = ELSE IF (TT VISC2 = END IF IF (P .LT. 25) THEN IF (TT .LT. 25) VISCI = ELSE IF (TT VISCI = ELSE IF (TT VISC1 = 550.9 + ELSE IF (TT .LT. 100 VISC1 = 384 ELSE IF (TT .LT. 150 VISC1 = 288.2 + ELSE IF (TT .LT. 200 VISC1 = 187.6 + ELSE IF (TT .LT. 250 VISC1 = 138.7 + ELSE IF (TT .LT. 300 VISC1 = 110.7 + ELSE IF (TT .LT. 350 VISC1 = 90.88 + ELSE IF (TT .LT. 375 VISC1 = 71.10 + ELSE IF (TT .LT. 400 VISC1 = 47.65 + ELSE IF (TT .LT. 425 VISC1 = 27.03 + ELSE IF (TT .LT. 450 VISC1 = 27.44 + ELSE IF (TT .LT. 475 VISC1 = 28.26 + ELSE IF (TT .LT. 500 VISC1 = 29.20 + ELSE IF (TT .LT. 550 VISC1 = 30.18 + ELSE IF (TT .LT. 600 VISC1 = 32.19 + TT-100)/50*(188.2-288.9) THEN TT-1501/50*(139.3-188.2) THEN TT-200)/50*(111.4-139.3) THEN TT-250)/50*(91.67-111.4) THEN TT-300)/50*(72.71-91.67) THEN TT-3501/25*(58.09-72.71) THEN TT-375)/25*(29.00-58.09) THEN TT-4 00J/25*(28.36-2 9.00) THEN TT-425)/25*(28.89-28.36) THEN TT-4501/25*(2 9.7 0-28. 89) THEN TT-4751/25*(30.61-29.70) THEN TT-500J/50*(32.54-30.61) THEN TT-550)/50*(34.50-32.54) THEN TT-600)/50*(36.4 5-34.50) THEN TT-6501/50*(38.38-36.45) THEN TT-700)/50*(40.26-38.38) THEN TT-750)/50*(42.11-4 0.26) ELSE IF (TT VISCI = ELSE IF (TT VISCI = ELSE IF (TT VISCI = ELSE IF (TT VISC1 = THEN 1744 + (TT-0)/25*(887.1-1744) .LT. 50) THEN 887.1 + (TT-25)/25*(550.9-887.1) .LT. 75) THEN TT-50)/25*(384-550.9) THEN + (TT-75)/25*(288.2-384) THEN TT-1001/50*(187.6-288.2) THEN TT-150)/50*(138.7-187.6) THEN TT-2001/50*(110.7-138.7) THEN TT-250)/50*(90.88-110.7) THEN TT-300)/50*(71.10-90.88) THEN TT-350)/25*(47.65-71.10) THEN TT-3751/25*(27.03-47. 65) THEN TT-4 00)/25*(27.4 4-27.03) THEN TT-4251/25*(28.26-27.44) THEN TT-4501/25*(29.20-28.26) THEN TT-4751/25*(30.18-29.20) THEN TT-5001/50*(32.19-30.18) THEN TT-550)/50*(34.20-32.19) THEN TT-600)/50*(36.18-34.20) THEN TT-6501/50*(38.12-36.18) THEN TT-700)/50*(40.03-38.12) THEN TT-750)/50*(41.89-40.03) .LT. 650 34.20 + .LT. 7 00 36.18 + .LT. 750 38.12 + .GE. 750 4 0.03 + 168 END IF END IF IF (P .GT. 25) THEN IF (TT .LT. 25) THEN VISC3 = 1735+ (TT-01/25*(886.6-1735) ELSE IF (TT .LT . 50) THEN VISC3 = 886 .6 + . (TT-251/25*(551. 8-886. 6) ELSE IF (TT -LT . 75) THEN VISC3 = 551 .8 + (TT-501/25*(385. 2-551. 8) ELSE IF (TT .LT . 100 THEN VISC3 = 385 .2 + (TT-75J/25*(289. 5-385. 2) ELSE IF (TT .LT . .150 THEN VISC3 = 289 .5 + (TT-1001/50*(188 .8-289.5) ELSE IF (TT .LT . 200 THEN VISC.3 = 188 .8 + (TT-150)/50*(139 .9-186 .8) ELSE IF (TT .LT . 250 THEN VISC3 = 139 .9 + (TT-200)/50*(U2 -139.9) ELSE IF (TT .LT . 300 THEN VISC3 = 112 + (TT-250)/50*(92.43 -112) ELSE IF (TT .LT . 350 THEN VISC3 = 92. 43 + (TT-300J/50*(74. 14-92. 43) ELSE IF (TT .LT . 375 THEN VISC3 = 74. 14 + TT-3501/25*(61. 87-74. 14) ELSE IF (TT .LT . 400 THEN VISC3 = 61. 87 + (TT-375)/25*(33. 73-61. 87) ELSE IF (TT .LT . 425 THEN VISC3 = 33. 73 + (TT-400)/25*(29. 70-33. 73) ELSE IF (TT .LT . 450 THEN VISC3 = 29. 70 + (TT-425)/25*(29. 71-29. 70) ELSE IF (TT .LT . 475 THEN VISC3 = 29. 71 + (TT-450)/25*(30. 32-29. 71) ELSE IF (TT .LT . 500 THEN VISC3 = 30. 32 + (TT-475)/25*(31. 12-30. 32) ELSE IF (TT .LT . 550 THEN VISC3 = 31. 12 + (TT-5001/50*(32. 93-31. 12) ELSE IF (TT .LT . 600 THEN VISC3 = 32. 93 + (TT-550)/50*(34 . 84-32. 93) ELSE IF (TT .LT . 650 ) THEN VISC3 = 34 . 84 + (TT-600)/50*(36. 75-34. 84) ELSE IF (TT .LT . 700 ) THEN VISC3 = 36. 75 + (TT-650)/50*(38. 64-36. 75) ELSE IF (TT .LT . 750 THEN VISC3 = 38. 64 + (TT-700J/50*(40. 51-38. 64) . ELSE IF (TT .GE . 750 THEN VISC3 = 40. 51 + (TT-750)/50*(42. 35-40. 51) END IF END IF IF (P .LT. 25) THEN VISC = VISC1 + (P-22.5)/2.5*(VISC2-VISC1) END IF IF (P .GT. 25) THEN VISC = VISC2 + (P-251/2.5*(VISC3-VISC2) END IF IF (P .EQ. 25) THEN VISC = VISC2 END IF VISCOSITY = VISC RETURN END C The r e s t of the program i s EQTEST.F, PRUSS and WAGNER'S C steam thermodynamic property program. Q « » t * t * 4 * H 4 4 t » . * * . * * H 4 * H * t t « » t * * 4 * * t » * t * 4 * H * * * » t t t t « 4 H t t * * t * 169 

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