XA0101453 IAEA-CMS-11 No.11 Residence Time Distribution Software Analysis User's Manual International Atomic Energy Agency, 1996 PLEASE BE AWARE THAT ALL OF THE MISSING PAGES IN THIS DOCUMENT WERE ORIGINALLY BLANK COMPUTER MANUAL SERIES No. 11 Residence Time Distribution Software Analysis User's Manual INTERNATIONAL ATOMIC ENERGY AGENCY, VIENNA, 1996 The originating Section of this publication in the IAEA was: Industrial Applications and Chemistry Section International Atomic Energy Agency Wagramerstrasse 5 P.O. Box 100 A-1400 Vienna, Austria RESIDENCE TIME DISTRIBUTION SOFTWARE ANALYSIS USER'S MANUAL IAEA, VIENNA, 1996 IAEA-CMS-11 ©IAEA, 1996 Printed by the IAEA in Austria December 1996 FOREWORD Since its introduction into chemical engineering by Danckwerts in 1953, the concept of residence time distribution (RTD) has become an important tool for the analysis of industrial units (chemical reactors, mixers, mills, fluidized beds, rotary kilns, shaft furnaces, flotation cells, dust cleaning systems, etc.). In spite of its "old age", the general and practical aspects of RTDs are still discussed in leading chemical engineering journals. Radiotracers are widely used in analysing the operation of industrial units to eliminate problems and improve the economic performance. Radiotracer applications cover a wide range of industrial activities in chemical and metallurgical processes, water treatment, mineral processing, environmental protection and civil engineering. Experiment design, data acquisition, treatment and interpretation are the basic elements of tracer methodology. The application of radiotracers to determine impulse response as RTD as well as the technical conditions for conducting experiments in industry and in the environment create a need for data processing using special software. Important progress has been made during recent years in the preparation of software programs for data treatment and interpretation. The software package developed for industrial process analysis and diagnosis by the stimulus-response methods contains all the methods for data processing for radiotracer experiments. The UNDP/RCA/IAEA Regional Project for Asia and the Pacific RAS/92/073 has placed strong emphasis on the development and applications of tracer technology. This RTD software manual for data analysis of radiotracer experiments is the product of activities undertaken in the context of this project. The manual is likely to be of wide interest for developing skills and confidence prior to the carrying out of field work. The software has been field tested and is in use in several Member States in experiment design and data analysis for a wide range of dynamic processes in industry, hydrology and environment. The manual is a suitable handbook for tracer activities in almost all types of applications and is intended for engineers and technicians as well as for end user specialists working in partnerships with the tracer groups. The case studies described in the manual deal with typical problems in industry and the environment common to all countries. The manual and the software were reviewed at the Expert Advisory Group Meeting on Mathematical Modelling of Tracer Flow Experiment held in Beijing, China, from 7 to 12 May 1995 as well as at two Expert meetings held in Taejon, Republic of Korea, from 18 to 23 September 1995 and in Wellington, New Zealand, from 4 to 8 December 1995. It is expected that this manual with the accompanying software diskettes will be a useful guide to scientists involved in the development and routine application of nuclear techniques in the diagnosis and analysis of processes. The manual and the software were prepared for publication by R. Zitny and J. Thyn, from the Czech Technical University in Prague. EDITORIAL NOTE In preparing this publication for press, staff of the IAEA have made up the pages from the original manuscript(s). The views expressed do not necessarily reflect those of the governments of the nominating Member States or of the nominating organizations. The use of particular designations of countries or territories does not imply any judgement by the publisher, the IAEA, as to the legal status of such countries or territories, of their authorities and institutions or of the delimitation of their boundaries. The mention of names of specific companies or products (whether or not indicated as registered) does not imply any intention to infringe proprietary rights, nor should it be construed as an endorsement or recommendation on the part of the IAEA. The IAEA has made reasonable efforts to check the program disk(s) for known viruses prior to distribution, but makes no warranty that all viruses are absent. The IAEA makes no warranty concerning the function or fitness of any program and/or subroutine reproduced on the disk(s), and shall have no liability or responsibility to any recipient with respect to any liability, loss or damage directly or indirectly arising out of the use of the disk(s) and the programs and/or subroutines contained therein, including, but not limited to, any loss of business or other incidental or consequential damages. CONTENTS 1. INTRODUCTION 7 2. BASIC NOTIONS 10 3. RTD PROGRAMS 18 3.1. General concept 18 3.1.1. Data structures 20 3.1.2. Data editor 23 3.1.3. Operations 27 3.1.4. Graphics 31 3.2. RTDO data treatment 34 3.2.1. Theoretical fundamentals (time decay correction, time constant correction, background raise elimination, z-transformation for variable flow) 34 3.2.2. RTDO - Operations 40 3.3. RTD1 identification, recycle analysis, Fourier and Laguerre transformation 42 3.3.1. Theoretical fundamentals (convolution, deconvolution, recycle, frequency analysis, correlation) 42 3.3.2. RTD1 - Operations 52 3.4. RTD2 modelling by means of differential equation system (system identification by means of regression analysis) 66 3.4.1. Theoretical fundamentals (numerical integration - Euler and Runge Kutta methods and nonlinear regression) 66 3.4.2. RTD2 - Operations 71 4. TASKS 79 4.1. RTDO 79 Task: T01 Introduction to RTDO, import of data, corrections, variable flow rate 79 4.2. RTD1 85 Task: Til Introduction to RTD1, import of data, interactive processing of time curves, computation of moments 85 Task: T12 Impulse response identification using splines, FFT and Laguerre functions 90 Task: T13 Identification of a system with recycle loop 98 4.3. RTD2 104 Task: T21 Introduction to RTD2, system description using differential equations 104 Task: T22 Identification of model parameters by nonlinear regression 109 Task: T23 Simulation of adiabatic reactor 115 LIST OF SYMBOLS 120 REFERENCES 121 APPENDIX I: CATALOGUE OF RTD MODELS 125 A. Simple two units models 127 B. Models - series 140 C. Models - backmixing 151 D. Parallel flows 158 E. Recirculating flows . 164 F. Models for special applications 169 G. Axial dispersion models 175 H. Convective models 181 APPENDIX II: LIST AND DESCRIPTION OF INPUT/OUTPUT VARIABLES (used in journal, labels, input panels) 187 APPENDIX III: APPLICATIONS OF RTD PROGRAMS 193 in.l. Steam velocity measurement - calibration of a Venturi meter 193 (Comparison of mean residence time and time delay) 111.2. Production of ethyl alcohol 199 (Application of exponential regression for parallel flow analysis) 111.3. Glass industry .201 (Frequency characteristic - gain = amplitude ratio) 111.4. Equalization of variations in impurities in waste water treatment 202 111.5. Analysis of gas flow in a pressurized fluidized bed combustor 204 (Process control in stationary conditions) 111.6. Production of aldehydes 207 (Control during production increase) 1117. Process of crushing and screening in a hammer mill . 211 (Modelling of comminution process of cereal grain) III.8. Biological activation process - waste water treatment 215 (Identification, system with recirculation, modelling) 1. Introduction The Residence Time Distribution (abbr. RTD) is an important characteristic of many continuous systems (e.g. chemical apparatuses: reactors, absorbers, filters, ...), which describes exactly what its name says: The residence time distribution of particles flowing through the investigated system (under steady state condition). This distribution is a function of residence time t (we adopt notation E(t)) defined in the following way Bit) - 1 inn W Q AA/.o A' 6* where Q [m3.s'2J is the total flowrate while q(t) is the flowrate of particles having residence time (the time they spent in a system) less than t. In the case of turbulent flows the flowrate q(t) is a stochastic quantity and its expected values have to be considered. The E(t) function can be also understood as a probability distribution: E(t) At is the probability that a particle randomly taken from the system outlet has the residence time between t and t+At. This RTD can be directly measured by injecting a unit impulse (unit amount of labelled particles) into the inlet of a system. As soon as the tracer has exactly the same flow properties as the other particles and thus follows the same paths, the tracer concentration c(t) registered at the outlet in time t is directly proportional to the value E(t) (more precisely: E(t) is proportional to the number of particles detected per unit time). It is of course impossible to realize an infinitely short injection of a finite number of labelled particles into an infinitely small (and ideally mixed) volume. Therefore the stimulus-response experimental technique must consider an imperfect pulse (deterministic or stochastic1) as a stimulus function and identify the impulse response E(t) by some computational procedure (this is the main job of the RTD1 program). Comment: Radioisotopes, which closely match the properties of a substance, are probably the best but are also most demanding tracers. Others, such as electrolytes or dyes, have the advantage in simplicity of sensors, nevertheless they are not very suitable for the harsh conditions of industrial plants (high temperatures etc.). The RTD can be used in a variety of ways: 1. Characteristic features of the E(t) course (e.g.