Tritium Removal Facility High Tritium Distillation Simulation

Transcription

1 Tritium Removal Facility High Tritium Distillation Simulation by Polad Zahedi A thesis submitted in conformity with the requirements for the degree of Master s of Applied Science Department of Mechanical and Industrial Engineering University of Toronto Copyright by Polad Zahedi 2011

2 Tritium Removal Facility High Tritium Distillation Simulation Abstract Polad Zahedi Master s of Applied Science Department of Mechanical and Industrial Engineering University of Toronto 2011 A dynamic model was developed for the distillation mechanism of the Darlington Tritium Removal Facility. The model was created using the commercial software package MATLAB/Simulink. The goal was to use such a model to predict the system behaviour for use in control analysis. The distillation system was first divided into individual components including columns, condensers, controllers, heaters and the hydraulic network. Flow streams were then developed to transfer enthalpy, pressure and mass flow rate between the components. The model was able to perform various plant transients for validation and analysis purposes. A comparison of the different controllers was made with the introduction of various disturbances to the system. Also, the effect of the system disturbances when isolated from the transients was studied using the same controllers. Studying different plant transients and disturbances under each controller enabled a comparative analysis. ii

3 Acknowledgments I would like to thank my supervisors, Dr. Majid Borairi and Dr. Javad Mostaghimi, for the aid and guidance they have provided throughout this work. Their knowledge and expertise have helped greatly in carrying out my project. Also deserving thanks is Brian Babcock from Ontario Power Generation whose technical support and guidance have been essential for this work. iii

4 Table of Contents Acknowledgments... iii Table of Contents... iv List of Tables... vi List of Figures... vii List of Appendices... ix Nomenclature... x Glossary... xii 1. Introduction Objectives Problem Statement System Description Darlington Tritium Removal Facility High Tritium Distillation Flooding Event HTD Control General Measurements Heater Control Mathematical HTD Model Assumptions and Limitations Hydraulic Network Theory The Hydrodynamic Network Model Basic Equations Columns iv

5 4.4 Hydraulic Network Condensers Control System Description Implementation and Validation of the Model Process Model Implementation Control Model Implementation Validation of the Steady State Results Validation of the Transient Results Discussion of the Results Conclusions Bibliography Appendices v

6 List of Tables Table 1 Physical Specification of the HTD Columns 31 Table 2 Color Representation of the system overview 31 Table 3 Color Representation of the Column Model 31 Table 4 Color Representation of the Control System Model 32 Table 5 The Design and Simulated steady state values of the Flow between the Columns 32 Table 6 The Design and Simulated steady state values of the Columns Pressure 32 Table 7 Column 1 Control Parameters 33 Table 8 Column 2 Control Parameters 33 Table 9 Column 3 Control Parameters 33 vi

7 List of Figures Figure 1 Block Diagram of DTRF Process 34 Figure 2 Tritium Removal Facility, Catalyst Exchange and Distillation 34 Figure 3 Tritium Removal Facility, Flow Diagram 35 Figure 4 High and Low Tritium Distillation Columns 36 Figure 5 Normal Packing Configuration 37 Figure 6 Packing Configuration during Flooding 38 Figure 7 Heater Control, Wiring Diagram 39 Figure 8 Node/Link Figure 40 Figure 9 Nodal Representation of a Column 40 Figure 10 A PID controller Block Diagram 41 Figure 10 B Cascade Controller Block diagram 41 Figure 11 System Overview 42 Figure 12 Single Entry of Warning Mechanism 43 Figure 13 Column Overview 44 Figure 14 Control System Overview 45 Figure 15 Condenser 1 Level, Plant Data, Feb 14, Figure 16 Condenser 1 Level, Condenser 1, HTD Model 46 Figure 17 Column 1 Apparent Level, Plant Data, Feb 14, Figure 18 Column 1 Apparent Level, HTD Model 46 Figure 19 Condenser 1 Level, Plant Data, Jan 01, Figure 20 Condenser 1 Level, Condenser 1, HTD Model 47 Figure 21 Column 1 Apparent Level, Plant Data, Jan 01, Figure 22 Column 1 Apparent Level, HTD Model 47 Figure 23 Column 2 Apparent Level, Plant Data, Jan 27, Figure 24 Column 2 Apparent Level, HTD Model 48 Figure 25 PID Controller, No Fault, Column 1 49 Figure 26 Proposed Cascade Controller, No Fault, Column 1 49 Figure 27 Optimized Cascade Controller, No Fault, Column 1 49 Figure 28 PID Controller, Heater Fault, Column 1 50 Figure 29 Proposed Cascade Controller, Heater Fault, Column 1 50 Figure 30 Cascade Controller, Heater Fault, Column 1 50 Figure 31 PID Controller, Power Transducer Fault, Column 1 51 Figure 32 Proposed Cascade Controller, Power Transducer Fault, Column 1 51 Figure 33 Optimized Cascade Controller, Power Transducer Fault, Column 1 51 Figure 34 PID Controller, Column 1 52 Figure 35 Proposed Cascade Controller, Column 1 52 Figure 36 Optimized Cascade Controller, Column 1 52 Figure 37 PID Controller, Column 2 53 vii

8 Figure 38 Proposed Cascade Controller, Column 2 53 Figure 39 Optimized Cascade Controller, Column 2 53 Figure 40 PID Controller, Heater Fault for three columns, Column 2 54 Figure 41 Proposed Cascade Controller, Heater Faults, Column 2 54 Figure 42 Optimized Cascade Controller, Heater Fault, Column 2 PID Controller, 54 Transducer Fault for three columns, Column 2 Figure 43 PID Controller, Transducer Fault for three columns, Column 2 55 Figure 44 Proposed Cascade Controller, Power Transducer Fault, Column 2 55 Figure 45 Optimized Cascade Controller, Power Transducer Fault, Column 2 55 viii

9 List of Appendices Tables 31 Figures 34 ix

10 Nomenclature W = Mass Flow (kg/s) m = Mass (kg) E = Energy (J) t = Time(s) Q = Rate of Heat Transfer (w) h = Enthalpy (J) V = Volume ( ) Specific Volume ( ) u = Specific Internal Energy (J/kg) P = Pressure (Pa) ρ = Density ( ) x = Steam Quality SUBSCRIPTS: I = Input Port from the Condenser to the Column O = Output Port from the Column to the Condenser N = Input Port from the Next Column P = Output Port to the Previous Column B = Boiling C = Condensation D = Liquid Node of the Column U = Gas Node of the Column = Intermediate Lower Node of the Column, may contain gas = Intermediate Upper Node of the Column, may contain liquid x

11 T = Total Combination of the Column Nodes sat = Saturation l = liquid g = gas xi

12 Glossary AU CD CRS DCS DMS DTRF DU FTS HTCB HTD IMC LTCB LTD OPG PID QDR RS SCR TRF TRIAC VPCE Adsorber Unit Condensation Cryogenic Refrigeration System Distributed Control System Deuterium Make-UP System Darlington Tritium Removal Facility Dryer Unit Feed Treatment System High Tritium Cold Box High Tritium Distillation Internal Model Control Low Tritium Cold Box Low Tritium Distillation Ontario Power Generation Proportional Integral Derivative Quarter Decay Ratio Recombiner System Silicon Control Rectifier Tritium Removal Facility Triode for Alternating Current Vapour Phase Catalytic Exchange xii

13 1 1. Introduction 1.1 Objectives The objective of this study is to evaluate the effectiveness of the three different configurations for the High Tritium Distillation (HTD) controller and assess their impact on the overall plant performance. In particular, the current PID controller and two different cascade control configurations are modeled and their effect on the apparent mismatch between the controller output and the heater are evaluated. 1.2 Problem Statement Darlington nuclear station has experience some undesirable behaviour in their HTD system due to poor performance of the level controllers in the three columns of the Tritium Removal Facility (TRF). Specifically, the sudden reduction of the column levels, level oscillations that happen simultaneously and individually in sequence and also negative level indications are major concerns. Furthermore, the electrical heaters which provide heat to the columns do not follow the output of the controllers received as 4-20 ma signals. For example, the heater wattage appears to be lower than expected in some cases and spikes are observed in the heater wattage.

14 2 2. System Description 2.1 Darlington Tritium Removal Facility The Darlington TRF (DTRF) is operated by Ontario Power Generation (OPG) and is designed to remove tritium from the heavy-water systems of all its CANDU reactor units. DTRF is capable of processing 2.5 Gg of heavy-water annually and extract tritium with a purity >99%, at an average tritium activity of 370 GBq/kg (10 Ci/kg ). The annual heavy-water-processing rate corresponds to a tritium extraction rate of 2.5 kg( )/year. Unlike any other civilian tritiumhandling facility in the world, the DTRF functions very much like a production facility. A schematic diagram of the DTRF process is shown in Figure 1 in Appendix B. Tritium from heavy water is removed in two steps. In step 1, tritium from heavy water is transferred to a gas stream using an eight-stage vapour-phase-catalytic-exchange (VPCE) unit, and the detritiated heavy water is returned to service. The system will reduce and maintain lower levels of tritium in the Nuclear Reactor Moderator and Heat Transport Systems. This will result in lower radiation doses to operating personnel and reduce the level of radiation in any releases of heavy water to the environment. In step 2, the tritium-enriched stream from the VPCE is fed to a Condensation (CD) unit to separate tritium from. A three-column system is used to separate tritium from. The purity of the tritium product extracted is >99%. In nuclear reactors the tritium is found in chemical combination with deuterium and oxygen in the form of tritiated heavy water. The DTRF consists of a front-end composed of vapour phase catalytic exchange and a back-end system consisting of cryogenic distillation. The tritiated heavy water is contacted with a pure deuterium gas stream in the presence of a catalyst. This transfers the tritium from the water to the deuterium gas (actually a mixture of the three hydrogen isotopes, protium, deuterium and tritium). This gas is then distilled at cryogenic temperature to separate the tritium (See Figure 2 in Appendix B).

15 3 Figure 3 in Appendix B illustrates the TRF system and some of its major components such as: Feed Treatment System (FTS), Vapour Phase Catalytic Exchange (VPCE), Dryer Unit (DU), Adsorber Unit (AU), Low Tritium Distillation (LTD), High Tritium Distillation (HTD), Cryogenic Refrigeration System (CRS), Recombiner System (RS) and Deuterium Make-Up System (DMS) Feed Treatment System (FTS): The tritiated heavy water from the reactor is transferred to the TRF on a batch basis. From the feed tanks a continuous flow is passed through a feed treatment system which eliminates insoluble solids, gases and organic contaminants. This is done by passing the feed through a degassing column, an evaporator and condenser, activated carbon adsorbers and filters. Vapour Phase Catalytic Exchange (VPCE): The feed then passes to the Vapour Phase Catalytic Exchange (VPCE) cascade. This is a multistage counter current system with concurrent flow of heavy water vapour and deuterium gas within each stage. Each stage consists of an evaporator, superheater, catalyst vessel and condenser. The chemical reaction causing the transfer of tritium from heavy water to the deuterium gas stream is: DTO + DT + (1) The number of stages in the VPCE cascade is established by the required design detritiation factor (the ratio of the tritium concentrations in the feed and return streams respectively). The detritiated water flows to a product tank from which it is transferred back to the reactor systems periodically. Liquid ring compressors are used for compressing the deuterium gas which flows from the VPCE to the Dryer Unit and for compressing the return gas from the distillation columns to the VPCE. These were selected because could be used as the sealing and cooling liquid in the compressors. This assured that contamination of the deuterium gas with oil or some other compressor lubricant would not be a problem.

16 4 Dryer Unit (DU): After leaving the VPCE cascade, the deuterium gas stream enriched with tritium is compressed and passed through a regenerable dryer unit to remove the heavy water vapour carried over with the gas. Adsorber Unit (AU): The dried gas enters a vacuum insulated cold box (the Low Tritium Cold Box); it is cooled and passes through a cryogenic adsorber which extracts traces of nitrogen, oxygen and heavy water. It is then further cooled down to almost the deuterium saturation temperature before entering the low tritium distillation column. Low Tritium Distillation (LTD): The low tritium cold box contains a single column which enriches the less volatile tritium in the bottom part. The bottom product from this column is transferred continuously to the high tritium cold box. The tritium depleted deuterium stream leaving the upper section of the low tritium distillation column is recycled to the VPCE cascade. High Tritium Cold Box (HTCB): This cold box is equipped with three columns in series in which the tritium concentration increases progressively. These columns are of successively smaller diameters to minimize the inventory of tritium in the system. Tritium with an atomic purity of 99.9% is withdrawn from the bottom of the last column and transferred to the Tritium Immobilization System. Cryogenic Refrigeration System (CRS): This system produces the refrigeration necessary for cooling down and continuous operation of the columns. The hydrogen of the Cryogenic Refrigeration System is compressed by means of Sulzer oil free labyrinth piston compressors. The compressed gas is then cooled in counter current heat exchangers by transfer of sensible heat to the return stream. The low temperature process configuration of the Cryogenic Refrigeration System is fairly complex, reflecting its dual

17 5 functions as a cooling system and as a heat pump operating between the low tritium column reboiler and condenser. The refrigerant leaving the condenser warms up close to room temperature in the counter current heat exchangers mentioned above and returns to the compressor suction inlet. Recombiner System (RS): A Recombiner is provided to convert deuterium gas to water. This is required during regeneration of the nitrogen adsorber, and also whenever the low tritium column is used to in its secondary function of stripping protium from deuterium, in addition to being the first stage of the tritium concentration process. More importantly, the Recombiner is used to burn down the inventory of the LTD and HTD systems prior to an outage during which maintenance is to be performed with these systems to be opened to atmosphere. The recombiner is a combustion type unit in which the hydrogen is burned via a diffusion flame in a controlled atmosphere. Deuterium Make-Up System (DMS): A make-up electrolyzer is provided to produce the required inventory of deuterium for filling the VPCE, LTD and HTD systems before startup and to compensate for the losses of hydrogen isotopes from the system which result from protium extraction, adsorber regeneration and tritium draw-offs. The electrolyzer splits heavy water into deuterium and oxygen. The deuterium is admitted to the LTD/HTD/VPCE closed circulation loop and the oxygen can be utilized in the recombiner. 2.2 High Tritium Distillation The purpose of the high tritium distillation is to increase the /DT separation, convert deuterium-tritide to deuterium and tritium, and to achieve a bottom concentration which contains tritium with not more than atomic fraction of deuterium and protium. Figure 4 in Appendix B illustrates the schematic of the HTD and its major components.

18 6 The necessary reflux for the columns is drawn from the reboilers as vapour by the corresponding condensers. The slightly higher pressure in the subsequent column, which is necessary to compensate for the pressure drop of the interconnecting transfer lines, is provided by the static head of liquid in a hydraulic sealing siphon. The conversion of deuterium-tritide to deuterium and tritium takes place in a catalyst converter which operates at ambient temperature. The catalyst was originally supplied as Platinum on Charcoal, i.e., similar to the VPCE catalyst. However, during initial operation, blockage was experienced in the HTD process systems. A possible cause of this blockage was attributed to the formation of methane by the radiolytic action of tritium on charcoal, with the resultant freezing out. The catalyst was changed to platinum on alumina, and since then, blockage of the HTD process systems has not been experienced. A vacuum unit is provided to evacuate HTD. The exhaust gases pass an oil mist eliminator. They are collected in an exhaust holding tank. 1 Total reflux is the mode used for start up. Twenty-four hours after start up the tank is already purged five times thus recalculating at least 99% of the tritium inventory. The design of the separation cascade is optimized with respect to hold-up, Curie inventory, DT conversion, packing efficiency and column manufacture. This leads to a three fold cascade. The physical specification of the three columns is listed in table 1 in Appendix A. All columns are controlled in the same way: The heating power to the reboiler is controlled by a level controller. The reflux rate is controlled by the level of the liquid hydrogen in the head condenser. This level is adjusted according to the power consumption of the relevant reboiler heating elements. During total reflux, the pressure controller is hooked up to the level controller of condenser 1. In normal operation, the pressure is controlled by the pressure of the LTD column. 1 The contents of the exhaust holding tank may be directed to the Ail Cleanup System (if the hydrogen isotope concentration is high enough) or directly up the stack (if the hydrogen concentration is low).

19 Flooding Event Flooding in distillation columns has been defined as excessive accumulation of liquid inside the column or inoperability due to excessive retention of liquid inside the column and even a point where it is difficult to obtain net downward flow of liquid, and any liquid fed to the column is carried out with the overhead gas. While these descriptions appear to be similar at first glance, they actually describe different stages or degrees of flooding. Excessive accumulation of liquid may or may not cause inoperability, and inoperability may or may not carry the feed liquid out with the overhead gas. Figure 5 in Appendix B illustrates a cross section through a distillation column, filled with a structured packing, showing the liquid flow and vapor flow when the column is operating in normal condition. Liquid is flowing downward over the structured packing countercurrent to the upward flowing vapor. The vapor must follow a tortuous path; but, the void space in the packing is predominantly filled with vapor. The vapor is said to be the continuous phase. The upward flow of the vapor exerts an aerodynamic drag on the falling liquid. This drag force acts in opposition to the force of gravity and slows the flow of the falling liquid. When the relative flow rates of the vapor and liquid are such that the drag force is greater than or equal to the gravity force; then, the liquid stops flowing down the column. This condition is called flooding. Flooding can begin at any vertical location in the column. Figure 6 in Appendix B illustrates the same cross section through the column as Figure 5 except the column is flooding.

20 8 3. HTD Control 3.1 General The tritium/deuterium mixture enters the High Tritium Cold Box (HTCB) through a motorized valve and flows into the Condenser 1 where it is condensed using liquid hydrogen as a coolant (See Figure 4). From the Condenser 1, it flows through the first column, Column 1, into the bottom evaporator in the column where it is evaporated. The condenser level is controlled on the hydrogen side of Low Tritium Cold Box (LTCB); the evaporator level is also controlled. The level control is achieved by varying the power that is generated by an electrical heater. Part of the evaporated deuterium is directed to the second column, Column 2, where it is treated exactly in the same way as in column 1. From column 2, the deuterium flows to the third column, column 3, and is treated once again in the same way. The deuterium/tritium mixture which is leaving column 3 passes through heat exchanger 2 to be warmed up for the conversion reaction 2DT which takes place in the catalytic converter. The return stream from catalytic converter is passing through heat exchanger 2 to be cooled down again, before it is fed into the column 2. The deuterium leaves the HTCB coming from column 1 through a motorized valve. The HTCB is kept under high vacuum by the diffusion pumps and the roughing pumps. The exhaust (tritium containing) gases are collected in a tank. The helium extraction motorized valves and the total reflux motorized valve are closed during this operation.

21 9 3.2 Measurements The reboiler levels are measured indirectly using the aluminum block temperature; the lower the temperature of the aluminum block, the higher is the level. Two different physical effects are used to get a redundant measure: 1. Vapour pressure of neon (P-transmitter) 2. Electrical resistance (Diode) The two signals are compared and the lower temperature is used for control in the Level Indicating Controller. Since the level of the columns is not directly measured and is implied from the temperature of the column, this measurement will be called Apparent Level from here on. The apparent level indications are calculated based on the column temperature as follows: Column 1: (2) Column 2: (3) Column 3: (4) Where, T = the temperature in degrees Kelvin

22 10 Each column has a variable electrical heater connected to the bottom. The electrical heaters are placed in aluminum casings. 3.3 Heater Control The heater controller is the primary control mechanism controlling the level of each column. When it is required to reduce the level of a column, the heater associated with that column will be automatically turned up by the controller to provide more heat to increase the boiling within the column. When it is required to increase the column level, the heater will be automatically turned down. The control signal from the heater controller, in the form of 4-20 ma signal, is fed to the firing board. The firing board is a Silicon controlled Rectifier (SCR). The modulated pulse generated from the firing board is received by the Triode for Alternating Current (TRIAC) which in turn regulates the amount of current passing through the TRIAC from the power supply to the heater. The output of the TRIAC is also received by the Transducer for power measurement (See Figure 7 in Appendix B). 4. Mathematical HTD Model This section describes the details of the HTD mathematical model which is used to simulate the HTD transients. 4.1 Assumptions and Limitations The following assumptions are made for the HTD model: 1. The reflux flow from a column to the previous column is compressible turbulent gas flow. 2. The Catalytic Converter acts only as a part of the pressure drop of the Column 3 reflux to Column The temperature of deuterium entering Heat Exchanger 2 and leaving Catalytic Converter are assumed to be the same based on the design manual. 4. The flow through the internal reflux line that brings the reflux flow back to the column is negligible. 5. The fluid temperature change due to passing through the extension to the cold box, located in top right side of the cold box, is negligible. 6. The pressure listed in the design manual for the low tritium column can be used for the portion of the column connected to HTD. 7. The feed concentration is 10 Ci/kg.

23 11 8. The flow through the Heat Exchanger 1 and expansion tank are ignored in this model. Based on the design manual this flow is very small and it is only 1.64% of the total flow exiting column 1 of HTD. 9. The enthalpy drop in the pipes connecting the columns is negligible and ignored. 10. The change of deuterium density due to change in pressure within one time step of the simulation is assumed to be negligible. 11. Deuterium and Tritium are assumed to be ideal gases. Limitation: Due to the unavailability of the manufacturer s data for some of the components, the information from the most similar component from the same manufacturer was used. 4.2 Hydraulic Network Theory The purpose of the hydraulic network model is to predict the transient behaviour of the HTD during normal operation. This requires solving the mass and energy balances for a single fluid, one-phase, one dimensional flow. The implementation of these equations for a generic hydraulic network is described. Specific configurations for HTD system can then be developed using the techniques described for the generic model as a basis. The phenomena to be modelled that shall be validated include: Single fluid, one phase, one dimensional pressure flow dynamics including pressure characteristics, pressure losses due to friction, gravity pressure and fittings. Convective heat transport phenomena for the fluid as it travels through the network and exchanges heat with the heat exchangers. Thermodynamic properties of deuterium and tritium. In general, deuterium and tritium properties are required for the sub-cooled liquid region, and the saturated region.

24 The Hydrodynamic Network Model The physical flow network system is represented by nodes and links. Figure 8 in appendix B shows a block presentation of a node and its links. The link L k is assigned node N i as its initial node and N j as its terminal node. There are two kinds of flow paths. The normal circuit fluid flow passages are termed as the noncritical link from which no leakage is considered to take place. Therefore, the flow is governed by a onedimensional momentum balance equation of the form (5) Where, W k = mass flow (kg/s) p i, p j = pressures at the initial and terminal nodes respectively (Pa) t = time (s) F k = a general nonlinear function A node i may be associated with a finite number of links which either initiate from or terminate at i. Conditions of the node are governed by the mass and energy conservation equations Basic Equations Mass balance: (6)

25 13 Energy balance: (7) The mass and energy equations are solved for the node from which the mass, m, and energy, U, can be obtained. The node density is calculated by: ρ (8) Where, V i = node volume (m 3 ) Specific internal energy, u, is calculated by: (9) The Deuterium and Tritium properties are looked up from the thermophysical property tables obtained from National Institute of Standards and Technology. 4.3 Columns Each column was divided into two major nodes, the liquid and gas node. The bidirectional link between the two nodes allows boiling mass transfer from the liquid node to the gas node and condensation mass transfer from the gas node to the liquid node. The external ports of the column are connected to the appropriate nodes of the other columns (See Figure 9 in Appendix B). Conservation of the mass and energy are the main governing principles in the mathematical model of the columns. In addition to the accumulation of mass and energy based on the inflow and outflow from each port, the heat generated through the heater plays a dominant role in accumulation of energy in the column. In Column 3, due to relatively higher concentration of Tritium, the decay heat of the Tritium is also taken into account in the conservation of energy equation.

26 14 The amount of vaporization and condensation is determined by comparing the specific internal energy of the node with the saturation internal energy corresponding to the calculated pressure of that instance in time. Any excess energy contained in the liquid node is converted to gas through boiling while the lack of energy in the gas node is compensated through condensation (See Equations 21-24). In this approach, the change of deuterium density due to change in pressure within one time step of the simulation is assumed to be negligible. Therefore, the approximated volume of the liquid node will be used to calculate the volume of the gas node. Solving the conservation of mass and energy equations, the specific volume and specific internal energy are also calculated. With either of the two properties, the new pressure of the gas node can be calculated. The nodal configuration does not necessary agree with the geometric setup of the column. For instance, the liquid entering from the top of the column, in this case, will be directly entering the bottom node which is the liquid node. This does not affect the dynamics of the model as it is used only as a geometric convention. Figure 9 represents a nodalized configuration of a single column. The symbols used for each node or link are used as subscripts in the equations 2. The mathematical model of the Columns is as follows: Liquid Node (D): Conservation of Mass: dm dt D W W (10) I C W B Where, m = Mass (kg) 2 See the subscript section of the nomenclature for the description of the symbols.

27 15 W = Mass Flow (kg/s) t = time (s) Conservation of Energy: de dt D Q W h W h W h (11) I I C C B B Where, Q = Rate of Heat Transfer (w) h = Enthalpy (J) E = Energy (J) Volume: m D VD (12) ρl(sat) Where, V = Volume ( ) ρ = Density ( ) V U V V (13) T D Gas Node (U): Conservation of Mass: dm dt U W W W W W (14) N B P O C

28 16 Conservation of Energy: de dt U W h W h W h W h W h (15) N N B B P P O O C C From (14), (13): V U υ U (16) m U Where, = Specific Volume ( ) From (15), (14): E U u U (17) m U Where, u = Specific Internal Energy (J/kg) We assume: PD P U (18) Where, P = Pressure (Pa)

29 17 E m D D (1 x )u x u x D 0 (19) D sat(liquid) D sat(gas) Where, x = Steam Quality From (19): W x m (20) B D D E m U U (1 x )u x u x U 1 (21) U sat(liquid) U sat(gas) From (21): WC (1 x )m (22) U U

30 18 The above mathematical model assumes the column to be at saturation. In order to expand the model to take into account the superheated state of the simulation, the following expansion to the model has been added. Here, the heat capacity and the ideal gas law have been used to calculate the offset from saturation. If : (23) (24) Where, M = Molar Mass of Deuterium = R = Ideal gas constant = T = Temperature in degree Kelvin 4.4 Hydraulic Network Due to unavailability of the HTD plant data for flow, pressure and level measurements, the design data was used to calculate the hydraulic network properties. The design pressures and flows are given in the TRF Design Manual. From these flows and pressures the pipe resistances were calculated. Pipe resistance calculations took into account the concentration of different species in each stream. For compressible gas flow the following equation was used to calculate the conductivity 3 of each link: (25) 3 Conductivity of a link is analogous to electrical conductivity of a wire and is inversely proportional to the resistance of each link against the flow of fluid.

31 Condensers Condensers in HTD are affected by both the cooling side and the process side. For this reason, it is important to model them in a way that both cooling side and process side disturbances can be introduced for analysis purposes. These disturbances are artificially generated and incorporated into the model as inputs. Due to the lack of geometric information, especially with regards to the relative elevation of the condensers, the condensers are not modeled from first principles. Instead, a calculated value of heat transfer, based on the design description of the system, is used by the condenser model to calculate the flow through the condenser. (26) Where, = Flow of liquid out of the condenser Q = heat transfer (w) = enthalpy of vaporization 5. Control System Description In every control configuration, the controller is the active element that receives the information from the measurements and takes appropriate control actions to adjust the values of the manipulated variables. This section describes the use of three control schemes that are used in the simulation of the HTD dynamic transients: a. The existing Proportional Integral Derivative controller (PID controller) b. The proposed Cascade controller c. Cascade controller with optimized gains PID Controller: the PID controller is the most common form of feedback control. The PID control algorithm is derived from classical linear control theory and is used for single loop

32 20 systems. The PID algorithm consists of three basic modes, the proportional, the integral and the derivative modes. Digital controllers are often synthesized by approximating continuous controllers. The discretized PID controller using a simple approximation resulting in: Where, = control signal at sample time k = Initial Value of the Control Signal = Controller Gain = Integral Time (s) = Derivative time (s) = Sampling Interval (s) variable = Control Error (e = r-y), r is the reference variable, y is the process measured It must be noted that the integral term does not have to be calculated for all k since a running sum can be made and updated when the new error is calculated. The integral, proportional and derivative parts can be interpreted as control actions based on the past, the present and the future. The derivative part can also be interpreted as prediction by linear extrapolation. Figure 10A in Appendix B illustrates a block diagram of a simple feedback loop governed by a PID controller. The existing Controller implemented in the HTD system is a PID controller. This controller is modeled based on the manufacturer s manual of the Distributed Control System (DCS) along with the current operating control parameters. The existing controller is a discrete PID controller.

33 21 Cascade Controller: When a single-loop control does not provide acceptable control performance, an enhancement such as cascade control is used. Cascade control strategy combines two feedback controllers, with the primary controller s output serving as the secondary controller s setpoint. Figure 10B in Appendix B illustrates a schematic of a closed loop control system governed by a cascaded controller. In this study, the Proposed Cascade Controller is modeled based on the similar cascade controller scheme proposed for HTD based on the requirements provided by TRF Operations Group 4 as well as the proposed controller parameters. The power measurement of the column heater and the column temperature are the variables to be controlled by the inner loop and outer loop, respectively. Cascade controller with optimized inner loop control gain parameters: similar configuration for the cascade controller described above is used with an exception of using a higher value for the inner loop proportional gain to make the system response faster. This configuration is called Optimized Cascade controller from here on. The parameters of the outer loop PID controller were calculated using the Ziegler-Nichols Quarter Decay Ratio (QDR) method. Since these values were very close to the existing PID controller parameters, they were not modified in the model. The Internal Model Control (IMC) method was used to calculate the parameters for the inner loops. In selecting the appropriate gain values for the inner loop control parameters, special attention was made to make sure the system remains stable at all time specially in the presence of unwanted disturbances. The control parameters are listed in the Appendix A. 4 Unregistered document provided by Operations

34 22 6. Implementation and Validation of the Model 6.1 Process Model Implementation The TRF HTD model is built on the MATLAB/SIMULINK simulation package. MATLAB is a C based text structure programming language and SIMULINK is a graphic programming language and provides blocks that may be combined to create "subsystems" or "modules". The TRF HTD model development process (i.e. life-cycle) involves the use of modularity and encapsulation. Each module is developed and tested independently. Modules are integrated to form the overall TRF HTD model. This approach provides flexibility, process discipline, consistency, and reusability of the developed codes. The major HTD components are modeled within a high level subsystem visible on the system overview. Each component is placed in the system overview such that the configuration of the model resembles a flow diagram. The components are placed in their appropriate locations both with respect to the actual geometry of the plant and based on the flow diagram. (See Figure 11 in Appendix B) In order to validate the accuracy of the models, the parameters values are checked for several different transients. In the validation process, the simulation results were also examined against the assumptions listed in Section 3.1. A warning mechanism is developed to identify and report any violation of those assumptions. Each entry of the warning mechanism checks a condition under which one of the assumptions is valid. Physical boundaries of the system are also checked. Furthermore, in this warning mechanism if a single condition is violated then a flag will be raised and maintains its value until the end of the simulation. An additional entry has also been added that checks all the other entries and flags the existence of at least one warning in the system. A single entry of the warning mechanism has been shown in Figure 12 in Appendix B. In order to expand the model to take into account the column dry out, a dry out mechanism has also been added to the column model. The column dry out mechanism is activated once the heat supplied from the heater is exactly enough or exceeds the amount of heat needed to vaporize the

35 23 liquid inventory of the column plus the inflow of the liquid from the condenser. In this condition, the excessive heat is directly applied to the gas node. An overview of the column model is provided in Figure 13 in Appendix B. The colors of Table 3 in Appendix A present the major elements of the column model. 6.2 Control Model Implementation A switch is used to select the desired control types. The selected control type will be flagged in the initialization process. Figure 14 in Appendix B shows an overview of the control system model. Table 4 in Appendix A lists the colors presenting the major elements of the control system. 6.3 Validation of the Steady State Results The accuracy of the HTD model developed in this study was validated by: a. Comparing the steady-state response of the model vs. the design data from the design manual. Specifically, the absolute values of the flows between the columns and the pressures of each column were compared to design manual values b. Comparing various transient responses to the real data collected during normal HTD operation. However, there were two challenges to validation of the HTD model: 1. There was significant deviation between some plant and design data. 2. There was limited plant data. Table 5 and Table 6 in Appendix A provide a summary of the design and simulated steady-state values for the column pressure and the flow between the columns for the feed concentration of 10 Ci/kg 6.4 Validation of the Transient Results As the second stage of validation, external disturbances through the cooling side of condensers and through the LTD are introduced to the HTD system and the shape of the trend is validated against plant data. The disturbances added to the system model are selected from actual plant data occurrences.

36 24 Condenser Level Step up: A step increase in the condenser level is introduced and the resultant change in column level is compared to a similar plant transient. For the purpose of the following transient validations, it was assumed that the rate of heat transfer in the condensers is linearly related to the level of coolant in each condenser. The plant data for the column exhibits a faster response to the change in condenser level in comparison with the simulated response. For visibility purposes, the time scale associated with the simulated response is selected to be relatively shorter. (See Figures in Appendix B) Condenser Level Dip: A rapid decrease in condenser level is introduced and the resultant change in column level is compared to a similar station transient. (See Figures in Appendix B) Column Flooding: Distillation columns have known issues with moisture hold up and flooding. Due to the complex nature of this phenomenon, it is not modeled from first principles. The plant data trend is modeled as an artificial liquid build up within the column and the subsequent release. The same disturbance observed in plant apparent level is reproduced. (See Figures 23 and 24 in Appendix B) 7. Discussion of the Results This section introduces three control logic configurations and assesses their effectiveness to improve the dynamic responses of the HTD system to various operating conditions. The transients that are examined include normal condition when there is no fault in the system and also when system is subjected to fault in the heater and power transducer. The plant data did not provide enough information to identify the failure of set point tracking of the heater. This could be due to the fact that the heater response was only captured through the power transducer reading. The fault magnitude was too small to have a discernible impact on the

37 25 temperature. It could not be determined whether the fault originates in the heater, the firing board, the TRIAC or the power transducer. Thus, two different failure cases were examined. a. The failure was assumed and modelled in the firing board and TRIAC systems. This fault is called Heater Fault from here on. b. The failure was assumed to be due to the power transducer measurement. This fault is called Power Transducer Fault from here on. One of the most dominant transients known to be experienced by distillation columns is a liquid hold up phenomenon called Flooding. The effect of this phenomenon has also been captured by the model such that it matches the plant data. Condenser Level Step up: This transient is the same as the one explained in Section 5.4. The condenser level step up increases the amount of condensation in the condenser. This causes an increase in the liquid inflow to the column. The raise of liquid inflow to the column reduces the temperature of the column. As explained in Section 2.2, the lower the temperature of the aluminum block, the higher is the apparent level calculated from column temperature. Figures 25 to 27 in Appendix B show the condenser level step response transient for fault free system using the existing controller, the proposed cascade controller, and the optimized cascade controller. Evidently, the responses are almost identical. Note that the Apparent Level for all column levels is dimensionless. Apparent level is derived from temperature and is an estimation of the level trend not the absolute level value. Figure 28 shows the PID Controller with a heater fault which affects the overall temperature of the column. Hence, the effect of the fault is seen in the apparent level which is based on temperature. Figures 29 and 30 show a similar transient for the proposed and optimized cascade controllers. In principle, the cascade controller should have a favourable response to a heater fault since the heater fault is detected before the temperature disturbance. However, the inner loop gain in the proposed cascade controller is too small to make a visible difference. In Figure 30, due to higher inner loop gain, this difference is more visible. Figure 31 shows that since the PID Controller does not use the power transducer measurement, it is not affected by the fault. Figure 32 and 33 illustrates that in contrast to the PID Controller, the

38 26 fault in power transducer affects the control system and consequently the apparent level. The optimized cascade controller, due to higher gain on the inner loop, experiences more of this adverse effect. The relative magnitudes of the faults and the transients are obtained from plant data. The effect of the condenser transient is much larger than any of the introduced faults. LTD Pressure Drop: LTD pressure is stable. However, in order to analyze the new control, it is necessary to study the effects of various disturbances including the ones that are not common. For this purpose, a sudden pressure drop is introduced in the LTD and the response of HTD is shown. The introduced pressure drop in LTD causes an increased pressure difference between LTD Column and HTD Column 1. This increased pressure drop raises the flow from HTD Column 1 to LTD Column. The increase in the outflow from HTD column 1 decreases the pressure and temperature of Column 1. This is shown as an increase in the calculated apparent level. The level of column 1 is shown since it has the most immediate and largest response to an LTD pressure change. Figure 34 in Appendix B shows the response of the apparent level in Column 1 as the closest HTD column to LTD. The responses in Figures 35 and 36 are very similar to the ones in Figure 34. Column Flooding: This transient is the same as the one explained in Section 5.4. The column flooding starts by a gradual liquid build up in the packing of the column. This liquid build up causes the bottom of the column, where the temperature transducer is placed, to temporarily dry up increasing its temperature. This is followed by a sudden release of the liquid originally trapped in the packing. The liquid release will abruptly decrease the temperature returning the temperature to its original value. The calculated apparent level shows a gradual decease followed by a sudden increase.

39 27 Figure 37 illustrates the response of the apparent level in Column 2 when the column goes through flooding. The responses in Figures 38 and 39 are very similar to the response in Figure 37. Multiple Faults: To better understand the effect of the faults in the system heater faults were introduced at steady state. The faults are introduced to all three columns simultaneously and their magnitudes were increased for better visibility. The results are shown in Figures 40 to 45 in Appendix B. Figure 40 shows a heater fault introduced in column 2 as well as the cascading effect of both adjacent columns 1 and 3. Column 2 was selected in this case so that the cascading effect of fault on each side of it can be included. Figures 41 and 42 show similar trends. However, Figure 42, due to higher inner loop gain, shows a more favourable response to the disturbance as the magnitude of the disturbance has reduced by about 28%. In Figure 43 it can be seen that the PID Controller, having no input from the power transducer, is not prone to transducer faults. Figure 44 and 45 show the effect of transducer fault in the proposed and optimized cascade controllers. Since the power transducer measurement is used in the inner loop of the cascade controller, its fault affects the overall control of the apparent level. In contrast to the heater fault, Figure 45 shows a more unfavourable response due to higher inner loop gain. 8. Conclusions The assessment in this thesis investigated the effectiveness of three control configurations to improve the performance of the HTD system. Different system transients were simulated when there was no fault in the system and when system was subjected to some faults. The simulation results show that all three control schemes produce similar responses. The cause of the apparent mismatch between the controller output and the power transducer reading is unknown. This could be due to a fault in the components leading to the heater (Firing board or TRIAC), a fault in the power transducer or it could be an artefact of the data due to sampling.

40 28 In case of a fault in the firing board or TRIAC fault, the system response under a cascade controller shows a slight improvement 5. However, if the fault originates from the power transducer, the cascade control will create an adverse effect which is not present in the current control scheme. This is due to the fact that the fault introduced is present in the inner loop of the cascade controller where the PID Controller does not have this loop. In the PID Controller the power transducer output is not used and hence the PID Controller is not affected by the power transducer fault. Both the simulation results and the plant data indicate that the impact of the heater versus controller mismatch, whatever the cause may be, is negligible (e.g. Figures 28-33). It is not clear what impact the inner loop would have on the heater integrity if the column went dry. The heater resistance should increase when the liquid cooling is removed. This will increase the resistance and decreases the power input to the heater. At some point the heater input and output will balance. With the present architecture, the heater power is measured but not controlled so the control system does not increase the demanded heater power to compensate for the increased resistance. However, with the cascade control architecture the heater power input is measured and the system will increase the power to the heater. In summary: A cascade controller has shown no significant impact on the major transients A cascade controller can improve the transient if the heater is not tracking the controller (versus a measurement fault). However, the change is negligible compared to the major transients A cascade controller will introduce some negative features in case of power measurement fault. This is due to the fact that only in cascade control the power measurement is used in the inner loop and hence power measurement faults affect the overall response of the system. 5 The assumption is that the fault is additive. Other types of faults may or may not be corrected by cascade loop.

41 29 Bibliography Elmqvist, H., Tummescheit, H. & Otter, H. (2003). Modeling of thermo-fluid systems Modelica. Media and Modelica.Fluid. In Proceedings of the 3rd International Modelica Conference. Sweden. Bhambare, K.S., Mitra, S.K., & Gaitonde, U.N. (2007). Modeling of a coal-fired natural circulation boiler. Journal of Energy Resource Technology, Fong, C., William, D. & Wong, T. (1983). Darlington Tritium Removal Facility Process Design Description Anderson, S. (2008). Modeling of a Drum Boiler Using MATLAB/Simulink, Youngstown State University, 1-44 Aengel, Y. A., & Boles, M. A. (2006) Thermodynamics: An Engineering Approach. Boston: McGraw Hill. Crowe, C. T., Elger, D. F, & Roberson, J. A. (2001) Engineering Fluid Mechanics. Hoboken, NJ: John Wiley & Sons, Inc. Incropera, F., & Dewitt, D. (1990) Fundamental of Heat and Mass Transfer. Hoboken, NJ: John Wiley & Sons, Inc. Emerson Process Management, Rosemount (2000). Distillation Column Flooding Diagnostics with Intelligent Differential Pressure Transmitter, 4-9 Nicholas, P. & Cheremisinoff, P. (2000). Handbook of Chemical Processing Equipment, Butterworth-Heinemann, Woburn, MA, Norman, P. & Liebermann. (1991). Troubleshooting Process Operations, 3rd Edition, Pennwell Publishing Co., Tulsa, OK, National Institute of Standards and Technology. (2011). Chemistry WebBook, Thermophysical Properties of Fluid Systems

42 30 Bhambare, K.S., Mitra, S.K., & Gaitonde, U.N. (2007). Modeling of a coal-fired natural circulation boiler. Journal of Energy Resource Technology, Kruger, K., Franke, R. & Rode, H. (2002). Optimization of boiler startup using a nonlinear boiler model and hard constraints. In Proceedings of the 15th International Conference on Energy, Costs, Optimization, Simulation and Environmental Impact of Energy Systems (ECOS 2002), volume II, Berlin, Germany. Ang, K.H., Chong, G.C.Y., and Li, Y. (2005). PID control system analysis, design, and technology, IEEE Trans Control Systems Tech, King, M. (2010) Process Control: A Practical Approach. Wiley Tan, K.K, Wang, Q.G. & Chieh, H. (1999). Advances in PID Control. Springer-Verlag London, UK. Miller, J.M. & Quelch, J. (1995). Operating Experience with Tritium Accounting and Analysis Systems in Our Tritium-Handling Facilities, Fusion Technology, 28, 1050.

43 31 Appendices Tables: Table 1: Physical Specification of the HTD Columns Length Diameter Packing Column ft. 3 (pipe) SULZER CY Column ft. 1 (pipe) Dixon Rings Column ft. (pipe) Coils Table 2: Color Representation of the system overview (Figure 11) Colors Components Distillation Columns Condensers Controllers and Heaters Hydraulic Networks Level Transducers Flooding mechanisms Tritium Draw Out Mechanism Warning Mechanism Table 3: Color Representation of the Column Model (Figure 12) Colors Components Conservation of Energy Conservation of Mass Dry Out Mechanism Saturation Table Lookup Superheated Region Calculations Pressure and Internal Energy Calculation Boiling Flow Calculation Condensation Flow Calculation

44 32 Table 4: Color Representation of the Control System Model (Figure 13) Colors Components Outer Loop Cascade Controller Inner Loop Cascade Controller Heater Calculations Power Transducer Fault Mechanism Heater Fault Mechanism Control Scheme Switch Conventional Controller Pressures: Table 5: The Design and Simulated steady state values of the Flow between the Columns Design Value (Pa) Simulated Value (Pa) Percent Difference (%) Column Column Column Flows: Table 6: The Design and Simulated steady state values of the Columns Pressure Design Value (kg/s) Simulated Value (kg/s) Percent Difference (%) From Column 1 to LTD From Column 2 to From Column 3 to

45 33 Control Parameters: Column 1: Table 7: Column 1 Control Parameters PID Controller Cascade Controller Optimized Controller Outer Loop P Outer Loop I 7e e-004 7e-4 Outer Loop D Inner Loop P N/A Inner Loop I N/A e Inner Loop D N/A 0 0 Column 2: Table 8: Column 2 Control Parameters PID Controller Cascade Controller Optimized Controller Outer Loop P Outer Loop I Outer Loop D Inner Loop P N/A Inner Loop I N/A e Inner Loop D N/A 0 0 Column 3: Table 9: Column 3 Control Parameters PID Controller Cascade Controller Optimized Controller Outer Loop P Outer Loop I Outer Loop D Inner Loop P N/A Inner Loop I N/A e Inner Loop D N/A 0 0

46 34 Figures Figure 1: Block Diagram of DTRF Process D2 D2O DT Distillation Columns Power Plant DTO/D2 DTO T2 Figure 2: Tritium Removal Facility, Catalyst Exchange and Distillation

47 35 D2O DMS O2 O2 RS HDO/D2O D2 Expansion Tank CRS D2 D2/DT AU LTD VPCE HTD DU FTS D2O D2O/DTO T2 Figure 3: Tritium Removal Facility, Flow Diagram

48 36 LTD THD Column 1 Expansion Tank THD Column 2 THD Column 3 Condenser 1 Heat Exchanger 1 Condenser 2 Condenser 3 Heat Exchanger 2 Catalyst Converter Figure 4: High and Low Tritium Distillation Columns

49 Figure 5: Normal Packing Configuration 37

50 Figure 6: Packing Configuration during Flooding 38

51 39 L1 N TRIAC Firing Board 4 20 ma From DCI 4000 Fuse Fuse 120 VAC Class IV Supply To Heater Fuse Transducer 120 VAC Figure 7: Heater Control, Wiring Diagram

52 40 N i L k N j Figure 8: Node/Link Figure Figure 9: Nodal Representation of a Column

53 41 Control Loop Setpoint (r) Error (e) Control Signal (u) - PID Plant + Figure 10A: PID controller Block Diagram Outer Loop Inner Loop (r1) (e1) (u1) (r2) (e2) (u2) - PID - PID Power Transducer Plant + + r1 = Outer Loop Setpoint r2 = Inner Loop Setpoint e1 = Outer Loop Error e2 = Inner Loop Error u1 = Outer Loop Control Signal u2 = Inner Loop Control Signal Figure 10B: Cascade Controller Block diagram

54 Figure 11: System Overview (See Table 2 for color representation) 42

55 Figure 12: Single Entry of Warning Mechanism 43

56 Figure 13: Column Overview (See Table 3 for color representation) 44